UPDATE 9.11pm: The investigations at Grenfell Tower have led police to believe the "number of people missing, but as yet unaccounted for" has risen from 58, the Metropolitan Police said.
Releasing the first images from inside the burnt-out building, Commander Stuart Cundy said some of the victims may never be identified.
He said: "The conditions due to the fire damage verge on indescribable, which is why this will be such a lengthy operation taking weeks to complete.
"We must also prepare people for the terrible reality that some people may not be identified due to the intensity of the fire."
Mr Cundy added: "Sadly that work leads me to believe that the number of people missing, but as yet unaccounted for has risen from yesterday's figure of 58."
Releasing a tranche of footage showing the aftermath of the blaze, Mr Cundy said: "Today, police teams continue their support to families, and make enquiries to cross check the number of those missing.
"I have always said I will be accurate about what I know, so the next figure of those presumed dead and missing will be released tomorrow, Monday 19 June. The figure will be higher but I do not wish to speculate on that number today."
UPDATE 6.29pm: Residents who met the British Prime Minister in Downing Street following the Grenfell Tower fire have criticised estate managers of the building as having been "invisible in the aftermath of the tragedy".
The group, made up of victims, residents, community leaders and volunteers, said they were grateful to Theresa May for listening to their concerns but demanded "real action and immediate results" moving forward.
In a statement they criticised Kensington and Chelsea Tenant Management Organisation for its reaction to the disaster.
The group said: "In our meeting at Downing Street, we explained to the Prime Minister the anger of all residents towards the management of the estate over a long period of time, paving the way to this tragedy.
"With the exception of very few junior officers, the estate managers have been invisible in the aftermath of the tragedy."
The group, which spent two-and-a-half hours with Mrs May on Friday and Saturday, hit out at the "longstanding neglect" of council buildings in the area.
It said: "We are devastated by this tragedy. We are angry about the inadequacy of the response and the longstanding neglect of our buildings by the council and building management.
"We are grateful to the Prime Minister for listening to us and for the assurances she has given us but now we need to see real action and immediate results with centralised coordination of the relief effort with residents closely involved.
"The Government must also take a serious look at the neglect and chronic underfunding of social housing over decades."
They added that local residents should be "consulted at all stages and that we should be listened to" in dealing with the fallout from the tragedy.
Theresa May has announced that victims who have been left homeless will be given at least £5,500 from an emergency fund.
Residents will be given £500 in cash followed by a bank payment for the rest from Monday.
The Prime Minister insisted the Government was doing everything possible to help those caught up in the tragedy.
The money will come from the £5m fund announced by Mrs May on Friday.
No 10 said the £500 cash payment is already being handed out and further payments will be available from the Westway Centre and the nearby post office in Portobello Road.
Help will be given to residents who do not have bank accounts.
Mrs May said: "As we continue to respond to the needs of the community, our focus is on ensuring that all of those affected by this unimaginable tragedy get the right support as quickly as possible.
"My government will continue to do absolutely everything possible to help all of those affected through the difficult days, weeks, months and years ahead."
UPDATE 3.43pm: Anger in the aftermath of the Grenfell Tower fire comes after "years of neglect" by council and Government, London's mayor said, adding that stories of grief and heroism from the blaze will stay with him forever.
Sadiq Khan spent more than two hours at St Clement's Church in west London on Sunday, as a service remembered victims of the disaster.
He said it was "humbling" to attend before meeting with many members of the congregation as well as other people who turned up to speak to him.
Vowing to be the "champion of the people", he said lessons must be learned from the tragedy, which is feared to have claimed the lives of at least 58 people.
Speaking outside after the service, which he attended with his wife Saadiya, he said people are "angry not simply at the poor response in the days afterwards from the council and the Government, but the years of neglect from the council and successive governments".
He described a feeling among people that they have been treated badly and not understood by the council because some of them are "poor, some may come from deprived backgrounds, some may be asylum seekers and refugees".
Families who have lost their homes must be supported, grieving people must be helped and it must not be "so hard" for those who need help to find it, he said.
He added: "As the mayor of London, I will do my bit to be the advocate, to be the fighter, and to be the champion of these people."
Criticising those who may think there are too many rules and regulations, he called on them to "remember those who have lost their lives in a preventable accident that didn't need to happen, and the tragedy we're seeing is because of the consequences of mistakes and neglect from politicians from the council and from the Government."
UPDATE 2pm: Sadiq Khan has joined a congregation at a church service near Grenfell Tower.
The mayor of London arrived at St Clement's Church in the west of the city on Sunday morning as worshippers remember those who lost their lives and those who remain missing after the devastating fire.
Flowers and missing persons posters are taped to the gates of the church, while bags of donations are piled outside the door.
Mr Khan arrived with his wife Saadiya and walked silently into the church, which has been used as a relief centre in the wake of the blaze.
It is the same church where the Prime Minister met a group of victims, residents, volunteers and community leaders on Friday, as an angry crowd outside directed shouts of "coward" and "shame on you" towards her.
Theresa May held a meeting in Downing Street the next day with residents she had spoken to at the church.
Bishop Tomlin, who is speaking at Sunday's service, said after the meeting that residents left feeling they had been listened to.
Mr Khan left the church more than two hours later, having spoken to many members of the congregation as well as others who came in after the service to see him.
He said: "I've spent time with the local community, not just the Christian congregation, but members of all faiths here at the church, grieving, sharing their stories.
"And I've got to say some of the stories that I've heard will stay with me forever.
"I've heard stories of heroism, from Christians, from Muslims and from others, looking after their brothers and sisters, their neighbours and doing the job that we expect from this brilliant community because of the fantastic community that is here in this part of London."
UPDATE 12.25pm:Survivors of the Grenfell Tower blaze are being given just £10 to live on by the council, a volunteer has said.
West London film producer Nisha Parti, who has been helping victims in Kensington, said the cash is being given to those checking into hotels in the wake of Wednesday's blaze.
She said volunteers were unable to get hold of any money, despite huge donations of cash being made and Theresa May pledging £5 million in emergency funds.
Speaking on ITV's Peston on Sunday, she said: "Kensington and Chelsea are giving £10 to the survivors when they go to hotels.
"There is money pouring in from all these amazing volunteers, we can't get access to the money and we cannot get it to the families."
When asked why they couldn't get access to it, she said: "Because no one's telling us where it is.
"Victims were going to hotels, arriving at hotels, with no one from the council to greet them, to check them in, to give them clothes and food.
"Volunteers are now going to hotels with food packages, with cash that they're trying to find because they have nothing."
Kensington MP Emma Dent Coad said survivors were being repeatedly moved around.
She told BBC One's Sunday Politics: "We are still hearing stories of people not being allocated properly.
"There's one woman this morning and her child, they have been moved three times since Wednesday into different accommodation.
"That's absolutely appalling."
Jeremy Corbyn has renewed calls for empty homes to be taken over by the Government to house victims of the Grenfell Tower fire.
The Labour leader also criticised the official response to the tragedy, saying people should have been offered immediate accommodation similar to travellers who are offered hotels when their planes are delayed.
He urged the Government to consider requisitioning or using compulsory purchase orders for flats that are deliberately kept vacant, in a process known as land-banking.
Mr Corbyn told ITV's Peston on Sunday: "Occupy it, compulsory purchase it, requisition it - there's a lot of things you can do.
"But can't we as a society just think, all of us, it's all very well putting our arms around people during the crisis but homelessness is rising, the housing crisis is getting worse and my point was quite a simple one.
"In an emergency, you have to bring all assets to the table in order to deal with that crisis and that's what I think we should be doing in this case."
UPDATE 11,30am: Cladding used on Grenfell Tower blamed for spreading the blaze is banned in Britain, Philip Hammond has said.
The Chancellor said a criminal investigation would examine whether building regulations had been breached when the block was overhauled.
Mr Hammond said the public inquiry set up by the Government following the tragedy would also examine if rules had been broken.
He told BBC One's Andrew Marr Show: "My understanding is the cladding in question, this flammable cladding which is banned in Europe and the US, is also banned here.
"So there are two separate questions. One, are our regulations correct, do they permit the right kind of materials and ban the wrong kind of materials? The second question is were they correctly complied with?
"That will be a subject that the inquiry will look at. It will also be a subject that the criminal investigation will be looking at."
UPDATE 8.15am:The Home Office has assisted the family of Grenfell Tower victim Mohammad Alhajali in "making arrangements for their travel to the UK".
The 23-year-old Syrian refugee was the first fatality of the disaster to be formally identified by police.
More than 85,000 people have signed a petition calling for his parents to be granted visas for the UK so they can attend his funeral.
A Home Office spokesman said on Saturday: "We made contact with Mr Alhajali's family yesterday and assisted them in making arrangements for their travel to the UK in these terribly sad circumstances."
The petition was set up by family friend Mirna Suleiman, 26, who had been ringing around numerous hospitals, rest centres and the casualty helpline for news of his fate before discovering he had not made it out alive.
She chose to launch the campaign because as someone with Syrian family herself, she knows how difficult it is to obtain a visa for visits.
The Syria Solidarity Campaign posted on Facebook: "We're very pleased to announce that the family of Mohammad Alhajali received visas to come to the UK for Mohammad's funeral.
"It's not the kind of reunion anyone would have wanted, but we know it will be comforting for the family as they grieve for the loss of Mohammad together."
Mr Alhajali's family said in a statement: "Mohammad was a very amazing and kind person. He gave love to everyone. He came to the UK because he had ambitions and aims for his life and for his family.
"Our whole family will miss Mohammad dearly and he will never be forgotten.
"To God we belong and to him we return."
Mr Alhajali's older brother Omar - who was with him in the flat - survived the fire after they were separated on the way out.
The percentage of rejected visa applications for visits from Syria has soared after the country's devastating civil war began in 2011.
But the Home Office has established processes which allow it to consider visa applications outside the Immigration Rules on compassionate grounds.
EARLIER: British Prime Minister Theresa May has ordered more boots on the ground at the Grenfell Tower fire site after labelling the support given to families in the aftermath of the deadly blaze "not good enough".
Police said at least 58 people died, or are missing, presumed dead, after fire ravaged the 24-storey tower block in the early hours of Wednesday.
Commander Stuart Cundy of the Metropolitan Police warned that the death toll could rise further as he formally identified the first victim as 23-year-old Syrian refugee Mohammad Alhajali.
At 58 casualties, it would make the Grenfell Tower blaze the deadliest in the capital since the Second World War.
The Prime Minister, who "welled up" after hearing harrowing accounts from people caught up in the deadly fire, said there had been "huge frustrations" on the ground as people struggled to find information.
More than 250 firefighters tackled the blaze in north Kensington as London Fire Commissioner Dany Cotton said the scene looked like a "disaster movie".
Speaking to the Observer, she said crews did not follow normal practice, adding: "Had we just followed standard fire brigade procedures, we would not have been able to commit firefighters in and conduct the rescues we did."
Sixteen bodies have been taken to the mortuary after flames tore through the 1970s tower block - while 14 others have been recovered from the building.
Moving tales from those caught up in the disaster are continuing to emerge, including a five-year-old girl who was swept up by her mother's boyfriend as black smoke filled her seventh floor bedroom.
Thea West, who was rescued by Mickey Paramasivan, told the Sun on Sunday: "Mickey woke me up. He's my hero. He put me under his dressing gown and ran down the stairs.
"There was smoke everywhere and it was too strong. I could not breathe."
Mr Cundy said: "Sadly, at this time there are 58 people who we have been told were in the Grenfell Tower on the night that are missing, and therefore sadly, I have to assume that they are dead."
"That number 58 may change. I really hope it won't, but it may increase.
"My commitment to families is that as soon as we can, we will locate and recover their loved ones.
"The reason we had to pause the search and recovery yesterday was for the safety of our staff.
"We do not want another fatality arising out of this tragedy."
Police have appealed to anyone who may have escaped from the building, but has not yet come forward, to make themselves known.
When asked about the search, Mr Cundy replied that the officers had gone "all the way to the top" of the tower, and explained that the first phase was a visual search.
Mr Cundy said the police investigation into the blaze would look at the building and its refurbishment in 2016 and vowed to prosecute people if there was evidence.
The police are appealing to anyone with pictures or videos of the blaze to hand them in, as they may help establish not only where and how the fire started, but also how it spread.
Victims met the Prime Minister at Number 10 on Saturday evening and man representing the group said they had spoken about their "demands and what we expect".
Mrs May said she had fixed a deadline of three weeks for everybody affected to be rehoused locally.
She added: "I have ordered that more staff be deployed across the area, wearing high visibility clothing, so they can easily be found, dispense advice and ensure the right support is provided."
Family liaison officers are working with 52 families, and as soon as victims are identified, their loved ones will be told.
Mr Cundy said: "I absolutely understand the frustration of why figures haven't been released earlier. The reason for that - at one point, in terms of our casualty bureau, there were 400 people who were reported missing from Grenfell Tower.
"Grenfell Tower itself is 120 flats. We have worked tirelessly over the last four days to truly understand those that we know were there on the night."
Anger flared in the Kensington community over the weekend - with many protests taking place across the capital - as some accused the authorities of withholding information and responding inadequately.
Mr Cundy said: "The investigation will be exhaustive. My intention is that it will help provide answers.
"If, as we investigate, we identify issues that are a risk to public safety, we will not be waiting until the end of the investigation before we provide that information to the appropriate authorities.
"If there are any safety issues that we and experts that we will be using identify, we will share that immediately."