Specialist officers from the counter-terrorism squad are helping the investigation into the collapse of Sergei Skripal on Sunday, which has sparked fears of a poison plot.
Media reports named the 66-year-old, a former colonel in Russian military intelligence, as the man found unconscious on a bench in a shopping center in the southwestern English city of Salisbury.
Police said a man in his 60s and a woman in her 30s found with him are being treated for "suspected exposure to an unknown substance" and are in critical condition in intensive care in hospital.
A "major incident" was declared and the area remained cordoned off on Tuesday.
Britain's chief counter-terrorism officer, Mark Rowley of London's Metropolitan Police, said specialist members of his team were supporting the investigation.
"Clearly it's a very unusual case and the critical thing is to get to the bottom of what has caused this incident as quickly as possible," he told BBC radio.
Local police say they are keeping "an open mind."
Skripal was sentenced to 13 years in jail in Russia in 2006 for betraying Russian intelligence agents to Britain's MI6 secret service.
He was pardoned before being flown to Britain as part of a high-profile spy swap between Russia and the United States in 2010.
The incident made the front pages of almost all Britain's newspapers on Tuesday, with the Daily Mail speculating that Skripal may have been the target of a revenge "hit" by former colleagues.
However Lugovoi, who is an MP in the Russian parliament, responded to the British media reports by saying that Britain "suffers from phobias."
"Because of the presidential elections, our actions in Syria, the situation with Skripal could be spun into an anti-Russian provocation," he told Interfax news agency.