Sergei Skripal and his daughter Yulia are believed to have been poisoned in Salisbury by a nerve agent, Assistant Commissioner Mark Rowley of the Metropolitan Police said.
Mr Rowley said the poisoning was being treated as attempted murder and said the pair had been “targeted specifically”.
A police officer who was one of the first on the scene in Salisbury is critically ill in hospital, Mr Rowley said.
He said: "In summary, this is being treated as a major incident involving attempted murder by administration of a nerve agent.
"As you know, these two people remain critically ill in hospital.
"Sadly, in addition, a police officer who was one of the first to attend the scene and respond to the incident is now also in a serious condition in hospital.
"Wiltshire Police are, of course, providing every support to his family.
"Whilst we are now in a position to confirm that their symptoms are as a result of exposure to a nerve agent, I will not be providing further information at this stage about the exact substance which has been identified."
Speaking after a meeting of the British Government's emergency committee Cobra this morning, Home Secretary Amber Rudd said: "There will be more information published by the police this afternoon about the substance."
She added: "I want to make sure that this investigation responds to evidence, not to rumour, but I can reassure the public ... that all action is going to be taken to keep everybody safe."
"We need to keep a cool head and make sure that we collect all the evidence we can, and we need to make sure that we respond, not to rumour, but to all the evidence that they collect, and then we need to decide what action to take.
"We do know more about the substance and the police will be making a further statement this afternoon in order to share some of that.
"We must let the police carry on their work. They will share what they can this afternoon, but I'm sure there will be more updates as the investigation continues."
The Russian Foreign Ministry has said that the incident with double agent Sergei Skripal and his daughter Yulia in England is being "used to further incite anti-Russian campaign in Western media".
Mr Skripal, 66, and 33-year-old Yulia remain fighting for their lives in hospital after being exposed to a mystery substance which has triggered a diplomatic row and prompted crisis talks in Whitehall.
The British Government this morning called a meeting of its emergency committee Cobra, to be chaired by Home Secretary Amber Rudd.
The cross-departmental meeting - previously held after terror attacks to plot the Government's response to national emergencies - comes as relations between the UK and the Kremlin soured after Foreign Secretary Boris Johnson went on the offensive in the House of Commons.
A Russian Foreign Ministry spokeswoman, Maria Zakharova, said that "what happened to Skripal has been immediately used to further incite anti-Russian campaign in Western media".
She added that the allegations were intended to "further exacerbate relations between our countries".
At the UK Government's Cobra meeting, British Foreign Secretary Boris Johnson noted that this case had "echoes" of the death of Alexander Litvinenko, a Russian dissident who was fatally poisoned in London in 2006.
He said: "While it would be wrong to prejudge the investigation, I can reassure the House that should evidence emerge that implies state responsibility, then Her Majesty's Government will respond appropriately and robustly."
In a fresh sign of the deterioration in relations between the countries, Mr Johnson also claimed Russia is "in many respects a malign and disruptive force".
The Russian Embassy said it was "completely untrue" to suggest the country's special services were involved and criticised Mr Johnson for speaking "in such a manner as if the investigation was already over".
The Defence Science and Technology Laboratory in nearby Porton Down, which has state-of-the-art equipment to look for trace amounts of substances, is believed to be involved in examining what could have caused Mr Skripal and his daughter to fall ill.
British counter-terrorism detectives have urged anyone in Salisbury city centre on Sunday to come forward to help with the "missing pieces" in the probe into how a Russian double agent and his daughter fell critically ill.
As the high-profile investigation enters a fourth day, counter-terror officers have extended the cordon yet further after the pair were found unconscious in Salisbury, Wiltshire, shortly after 4pm on Sunday.
Assistant Commissioner Mark Rowley, the head of counter-terrorism policing, stressed to people in the city, particularly those who visited the Bishop's Mill pub or Zizzi restaurant, that any details could help investigators.
He said: "We would like to hear from anybody who visited the area close to the Maltings shopping centre where these two people were taken ill on Sunday afternoon, and may have seen something that could assist the investigation.
"The two people taken ill were in Salisbury centre from around 1.30pm. Did you see anything out of the ordinary? It may be that at the time, nothing appeared out of place or untoward but with what you now know, you remember something that might be of significance.
"Your memory of that afternoon and your movements alone could help us with missing pieces of the investigation. The weather was poor that day so there were not as many people out and about. Every statement we can take is important."
Scotland Yard said detectives were "keeping an open mind as to what happened", and that the situation had not been declared a terrorist incident - adding that it would not "provide a running commentary" on the investigation.
Mr Skripal was convicted in 2006 of passing state secrets to MI6 before being given refuge in the UK as part of a spy swap.
The former colonel in Russian military intelligence, who was sentenced to 13 years in prison, was among four convicts who were given pardons and one of two sent to Britain in 2010 in a deal that was said at the time to be the largest exchange since the Cold War.
He was found along with his daughter on a bench in The Maltings in Salisbury after police were called by a concerned member of the public at around 4.15pm on Sunday.
The pair did not have any visible injuries and were taken to Salisbury District Hospital, where they are being treated in intensive care for "suspected exposure to an unknown substance".
Officers "secured" a number of scenes - including the Zizzi restaurant on Castle Street and the Bishop's Mill pub in The Maltings - as well as setting up a cordon at Solstice Park in Amesbury, a business park around eight miles north of the city which is home to restaurants and an ambulance station.
Scotland Yard said: "This is linked to the investigation and is a precautionary measure."
At least two people left a contamination tent inside the cordon wearing protective suits and gas masks on Tuesday night.
People could also be seen inside Zizzi's restaurant wearing protective gear and masks.