Latest: The Metropolitan Police have released some details of the 12 people arrested in raids in east London today.
Here is a recap of how the terror unfolded:
What we know so far:
Update 10.54pm: Islamic State has claimed responsibility for Saturday's attack on London.
BBC News have reported that the group's news outlet Amaq, on the messaging app Telegram, said "a security unit of Islamic State fighters carried out the London attacks yesterday".
Update 10.24pm: The Metropolitan Police have released some details of the 12 people arrested in raids in east London today.
They have said that seven of those arrested are women and range in age from 19 to their 60s.
Five men have also been detained and they are between 28 and 55 years old.
They added that one man has been released without charge.
Police said they made 11 of the 12 arrests at a single property in Barking.
A 27-year-old man
A 28-year-old man
A 52-year-old man
A 55-year-old man
A 55-year-old man, who has since been released without charge
A 19-year-old woman
A 24-year-old woman
A 27-year-old woman
A 49-year-old woman
A 53-year-old woman
A 60-year-old woman
A 38-year-old woman was arrested at another house in Barking. They were all detained under the Terrorism Act.
They added that no arrests were made at two properties in Newham, but they did say that "a number of people have been spoken to".
Update 7.40pm: Leaders of the Muslim Council of Britain (MCB) have backed comments by Theresa May saying "enough is enough" after the London Bridge attack, and said they will be stepping up efforts to curb Islamic extremism in Britain.
Muslim community representatives from around the country were led by MCB secretary general Harun Rashid Khan, who condemned Islamic extremism as a "death cult", and said "British Muslims must play our part" in turning people away from the ideology.
He said: "Today's attack makes us all angry, it makes me angry. And we want to do something about it.
"That is why we agree with the Prime Minister that things must change.
"Enough is enough.
"We are ready to have those difficult conversations, as equal citizens with an equal stake in this fight.
"I am pleased that the Prime Minister is speaking about conversation, it implies that we must listen to one another and work together to be part of a truly United Kingdom."
Mr Khan said the MCB will now initiate a new campaign with mosques to report suspicious activity, and were "extending our hand of partnership and co-operation to the Government and Prime Minister".
He said: "We want to turn people's minds away from this death cult.
"We want to ensure families are not torn apart by being either victims of terrorist outrages, or finding out that someone they knew perpetrated such acts."
Update 6.16pm: The mother of a 23-year-old stabbed in the London terror attack has said he was approached by a man who said "this is for Islam" before sticking a knife in him.
Elizabeth O'Neill said her son Daniel was out with a friend and his girlfriend when he stepped outside the bar and was attacked.
Speaking to reporters outside King's College Hospital on Sunday she said: "He had just stepped outside the bar for a second and a man ran up to him and said 'this is for my family, this is for Islam' and stuck a knife straight in him.
"He has got a seven-inch scar going from his belly round to his back."
Ms O'Neill said her son went in to the pub after the attack and the man ran away.
She added: "There was shots fired, everybody was told to lie down and then they were told to go downstairs in the bar.
"At this stage, Daniel's friend had put a tourniquet on him and was holding pressure there."
She said he was taken downstairs and then the police took him in their car to the hospital and that she was trying to find those officers to thank them.
She added: "The police have been absolutely fantastic, the nurses, staff have been absolutely, absolutely amazing."
She said she and her son, who was able to talk to her, were still in shock and described the attacks as "absolutely senseless" and the attackers as "callous and barbaric" and "absolute cowards".
She added: "These people say they are doing it in the name of god which is an absolute joke."
Asked about her son's condition, she said: "We are not sure yet, the ultrasounds were good but he is still quite sick so we can't rule out any kidney damage."
Update 5.33pm: Armed police swooped on a flat in east London and dragged two suspects away, according to witnesses.
Dozens of officers carrying guns and with their faces covered were seen raiding a property above a shop in East Ham at around 2pm on Sunday.
Witnesses say two men were dragged out and taken away in police vans.
Local resident Malik Rouf, 30, said one of the men inside the flat jumped out of a first floor window on to a ledge before he was pulled back inside.
"He was about 30 years old and in a vest - he tried to go out the window but the officer was standing with a gun saying 'get back in, get back in'," he told the Press Association.
"He was dragged out and put in a police van."
He said both men had shaved heads, full beards and one was wearing Islamic robes.
A line of police tape was put in place around the flat and crowds of locals looked on as officers guarded the perimeter.
Witness Shimma Ali, 32, said it was terrifying to see dozens of armed officers in the street.
"I heard a woman screaming and 20 officers with guns - there was a sniper across the road trained on the window," she said.
"Then a young black man, barefoot and in pyjamas, came out the window.
"They were shouting 'we will shoot you if you don't go back in'.
"I thought he was going to get shot - the police officer had his gun on him and was ready to shoot."
She added: "It's absolutely terrifying - we don't expect it in this area, it's so multicultural and diverse, there's no racism."
Update 4.36pm: Eight police firearms officers fired an "unprecedented" 50 rounds at the three London Bridge terrorists, Assistant Commissioner Mark Rowley said.
A member of the public also received a gunshot wound.
"Whilst this will be subject to an investigation by the IPCC, our initial assessment is in the region of 50 rounds - in the region of 50 bullets - were fired by those eight officers.
"The three attackers were shot dead.
"The situation these officers were confronted with was critical - a matter of life and death - three armed men wearing what appeared to be suicide belts."
Mr Rowley added: "As the officers confronted a terrorist, a member of the public also suffered a gunshot wound.
"Although the injuries are not critical in nature, they are in hospital receiving medical attention."
Mr Rowley said 36 people were being treated in hospital for various injuries, a number of them "extremely serious".
Giving an update on the investigation outside New Scotland Yard, he said "significant progress" had been made in identifying the attackers.
It comes after police raids in east London, including activity at an address in East Ham on Sunday afternoon.
Mr Rowley revealed that the white Renault van used to target pedestrians on London Bridge had been "recently hired" by one of the terrorists.
He said that as well as more armed police across the capital "the public will also see an increased physical measures in order to keep public safe on London's bridges".
Update 4.04pm: A Canadian national was among those killed in the London Bridge terror attack, Prime Minister Justin Trudeau said.
Update 3.55pm: Just over a mile away on Barking Road in East Ham there is a heavy armed police presence but Scotland Yard is unable to say whether it is linked to the earlier arrests.
Update 3.37pm: NHS England says that 21 people injured in the London Bridge terror attack are in a critical condition.
The BBC are reporting that investigators have identitied the three attackers, but they are not likely to be officially named yet.
An off-duty Metropolitan Police officer was also seriously injured during the London Bridge attack, Scotland Yard said.
A spokesman said: "We ask you to be vigilant and report anything that you see or hear which is suspicious, or just doesn't feel right."
Metropolitan Police Federation chairman Ken Marsh said: "I can confirm that sadly some of our colleagues were among the injured in the attack last night. I join all UK police colleagues in wishing them a swift recovery.
"We are offering them our full support."
The British Government has announced that there will be a minute's silence across the UK at 11am on Tuesday morning to remember those affected by the London Bridge attack.
The silence will be marked at all government buildings and flags will remain at half-mast on Whitehall government buildings until Tuesday evening.
Update 1.32pm: Police investigating the London Bridge terror attacks which left seven people dead and dozens more injured have arrested 12 people.
They were detained after an armed raid in Barking, east London, the day after the van and knife rampage by three terrorists who were shot dead by police.
Scotland Yard said the investigation into the "horrific attack" at London Bridge and Borough Market was progressing rapidly with officers searching several addresses in the area.
The arrests in connection with the attacks came as British Prime Minister Theresa May warned that Britain is in the grip of a spate of copycat terror plots and it emerged that an off-duty Metropolitan Police officer was among the 48 people injured by the terrorists.
Update 1.05pm: Several people were detained by police during an armed operation at some east London flats where neighbours said one of the London Bridge attackers may have lived.
At least four police vans were stationed behind a cordon outside the Elizabeth Fry flats in King's Road, Barking, and residents reported hearing bangs on Sunday morning.
Some neighbours said a photograph of one of the attackers resembled a man who lived in one of the flats.
Veronica Oladapo, 45, who lives in the neighbouring Forresters Apartments, said she left her building at around 7am to see police taking four men and a woman away.
She said she saw two men and a woman being taken away by ambulance after other neighbours reported hearing shots fired, while two men were later led away by police.
She said: "When I came out they were already taking some of the casualties away.
"There were three of them ... the ambulance came and took them away.
"There were another two sitting down inside."
One of the men had a hood pulled over his head while another one used a jacket to hide his face, she said.
More than five hours after the first arrests, a woman in a burka was led into a police van parked outside the flats.
It then drove away with sirens blazing, followed by three other vans.
Update 12.59pm: A British Transport Police (BTP) officer was stabbed in the face as he responded to the terrorist incident at London Bridge.
Emergency services rushed to the scene following reports of a vehicle ploughing into pedestrians around London Bridge and stabbings at Borough Market shortly after 10pm.
The BTP officer, who was on duty, was one of the first on the scene after he responded to calls for help from the public, the force said.
A spokeswoman said it was believed he was targeted by one of the three attackers who were later shot dead by police.
BTP said in a statement: "He received injuries to his head, face and leg, which, at this time, are believed to be serious but not life threatening."
"The officer is currently being treated in a central London hospital and his family are with him while he receives treatment."
No other BTP officers are thought to have been injured in the incident.
Update 12.40pm: Police have carried out raids in Barking, east London, though the Met could not immediately confirm any link to the attacks.
Update 11am: Theresa May has warned that Britain is in the grip of a spate of copycat terror attacks in the wake of the London Bridge atrocity.
The Prime Minister delivered a stark assessment of the threat facing the UK after seven people were murdered and dozens more injured by three terrorists on Saturday night.
It was the third terrorist outrage to hit the country this year following the Westminster and Manchester attacks.
Speaking outside Downing Street, Mrs May said that although there was no direct link between the three incidents, "terrorism breeds terrorism".
The PM said: "This is, as we all know, the third terrorist attack Britain has experienced in the last three months.
"In March a similar attack took place just around the corner on Westminster Bridge.
"Two weeks ago the Manchester Arena was attacked by a suicide bomber and now London has been struck once more.
Theresa May's statement to the nation in full - go about your lives; terrorism will not win. pic.twitter.com/iz0I8dvE1a— Ryan Hooper (@RyanJHooper) June 4, 2017
"And at the same time the security and intelligence agencies and police have disrupted five credible plots since the Westminster attack in March.
"In terms of their planning and execution, the recent attacks are not connected but we believe we are experiencing a new trend in the threat we face.
"As terrorism breeds terrorism and perpetrators are inspired to attack, not only on the basis of carefully constructed plots after years of planning and training, and not even as lone attackers radicalised online, but by copying one another and often using the crudest of means of attack."
Update 10.20am: Witnesses said the terrorists drove into pedestrians on the bridge in the same way as Westminster Bridge attacker Khalid Masood.
They then emerged and attacked some of the people they had hit with the van before heading to Borough Market, where the pubs and restaurants were packed with Saturday night crowds, including many watching the Champions League final between Juventus and Real Madrid in Cardiff.
They were heard shouting 'This is for Allah' as they attacked people.
One woman, who was in Black and Blue restaurant, said: "We just saw three guys come into the restaurant, stabbed someone in the face and someone in the stomach.
"One of them had a big knife. Then he came in and walked around the restaurant. I guess they just kind of stabbed anyone that they saw and knocked things on the ground and then we just hid."
Barman Alex Martinez was forced to take shelter in a bin when a one knifeman entered El Pastor restaurant.
He said: "I saw that man with a knife in his hand and after that a man started screaming so I knew something wrong was happening.
London Police Commissioner gives London attack update: "This is a fast-moving investigation. We have very significant resources deployed" pic.twitter.com/ouPcbpuRQT— CNN International (@cnni) June 4, 2017
"The man started screaming and dropping everything on the floor, the plates, the cutlery, the bottle, everything, he dropped it."
Metropolitan Police Commissioner Cressida Dick gave details of how the incident unfolded.
"Our officers confronted the suspects and brought this terrible incident to a conclusion within eight minutes," she said.
"We were called at 10.08pm last night initially to reports that a vehicle had struck pedestrians on London Bridge.
"That vehicle continued to drive from London Bridge to Borough Market. The suspects then left the vehicle and a number of people were stabbed.
"The suspects were shot dead by armed officers."
She said she understood it was a "worrying time" and "there is going to be considerable concern by some people, and fear indeed amongst some people".
The commissioner added: "What I think we are asking for is that people do not overreact.
"People of course will make their own decisions about what they do or don't do.
Lord Brian Paddick, fmr deputy assistant commissioner: "Police have armed response vehicles all over London, ready to respond to incidents" pic.twitter.com/IvKE8iRdRs— CNN International (@cnni) June 4, 2017
"But the last thing we need is people overreacting or beginning to take out their frustrations on other people in other communities or in their own communities.
"So we would like people to allow the police and the intelligence agencies to get on with their work and to remain calm.
"And of course we would want people, where they feel able to, to carry on with their normal lives."
Update 9.44am: Metropolitan Police Commissioner Cressida Dick said the number of victims from the London attack has risen to seven.
Commissioner Dick condemned the atrocity as "appalling" and "ghastly".
She said police believe there were three attackers and that all had been "neutralised".
Earlier: Three men have been shot dead after killing six and injuring 48 more with a van and knife attack in London.
The killings on Saturday night were the second terrorist atrocity to hit the country in as many weeks after 22 were killed at an Ariana Grande concert in Manchester.
Attackers brought carnage to the streets of the capital, stabbing a police officer and revellers with 12-inch knives, reportedly shouting "this is for Allah".
The trio were pictured wearing what appeared to be explosive vests, with Scotland Yard later confirming they were hoaxes.
Witnesses reported seeing a vehicle travelling at about 50mph strike people walking along the pavement.
Holly Jones, a BBC reporter, who was at London Bridge, said: "A white van driver came speeding - probably about 50mph - veered off the road into the crowds of people who were walking along the pavement.
"He swerved right round me and then hit about five or six people. He hit about two people in front of me and then three behind."
Witness Eric described the terror attack as a "rampage".
He told BBC Radio 5 Live he saw three people get out the van and initially believed they were going to help those who had been injured.
He said: "The three people literally started kicking them, punching them, and took out knives. It was a rampage really."
The three men ran off towards the nearby bars and restaurants and there was a shout of "this is for Allah", he told the station.
Another witness called Gerard said the suspects stabbed a series of people near Borough Market and shouted, "This is for Allah".
Liam Connell was in Katzenjammers Bierhall in Southwark Street, where customers were told to evacuate by staff before armed police told them to get on the ground.
He told the Press Association: "Then someone came in off the street and he had a white cuff around his neck.
"(The man) said he had been stabbed in the neck and I was holding his bandage and wound while he was talking to the police."
Guy's and St Thomas' NHS Foundation hospital said it was "on lockdown" to keep patients, relatives and staff safe, while a picture on social media showed armed police outside the Andaz Hotel in Liverpool Street, where the walking wounded were reportedly taken.
London Ambulance Service Assistant Director of Operations Peter Rhodes said: "We took 48 patients to five hospitals across London and treated a number of others at the scene for minor injuries."
Assistant Commissioner Mark Rowley of the Metropolitan Police said: "At this stage, we believe that six people have died in addition to the three attackers shot dead by police. And at least 20 casualties have been taken to six hospitals across London.
"We believe three people were involved but we still have some more inquiries to be 100% confident on that."
He added officers were treating the incident as terrorism and additional police would be deployed in the capital.
Police have opened a casualty bureau line for people concerned about loved ones on 0800 0961 233.
The attack has received widespread condemnation from political leaders, with London mayor Sadiq Khan calling it "deliberate and cowardly".
He said: "This was a deliberate and cowardly attack on innocent Londoners and visitors to our city enjoying their Saturday night.
"I condemn it in the strongest possible terms. There is no justification whatsoever for such barbaric acts."
Prime Minister Theresa May said: "Our thoughts are with those who are caught up in these dreadful events."
The Government's Cobra emergency committee will meet on Sunday, Downing Street said.
Media in France reported that two French citizens were injured in the attack.
A statement from the Elysee said: "The attack which struck London, days after that which took place in Manchester, is a new abominable and cowardly attack against our free society.
"Fellow French citizens are among the injured. France is putting everything in place to assist them."
Statement from Assistant Chief Constable Garry Shewan ahead of today's events. pic.twitter.com/hlAK7MUEOf— Greater Manchester Police (@gmpolice) June 4, 2017
BBC reporter Holly Jones was at the bridge when the incident happened, and was told by an injured French woman that she did not know where the two people who had been with her were.
Ms Jones said: "She told me in French: 'I don't know where those two other people are.' So the police are checking the Thames.
"They were right near the edge of the bridge. It looks potentially they could have been thrown over."
Fourteen people injured in the attack were taken to King's College Hospital, in Denmark Hill, south London.
A spokesman said: "The Emergency Department at King's College Hospital (Denmark Hill) received 14 casualties (six females and eight males) following the incidents at London Bridge and Borough Market in central London.
"One patient has been discharged."
French foreign minister Jean-Yves Le Drian told radio station FranceInfo four French citizens were injured in the attack.