A pizza restaurant in Salisbury was closed by police late on Monday night as Sergei Skripal, 66, fought for his life in hospital a day after he was found unconscious in the Wiltshire city.
The BBC named Skripal as the man who was found along with a woman in her 30s, believed to be known to him, on a bench near a shopping centre shortly after 4pm on Sunday.
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 the 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.
Wiltshire Police said officers were as yet "unable to ascertain" whether the pair, who are both in critical condition in intensive care, have been victims of a crime.
The Castle Street branch of the chain restaurant Zizzi was "secured as a precaution", the force said, adding Public Health England believed there was no risk to the public.
Officers in regular uniforms and plain clothes spoke to staff inside and worked in tents in the area the pair were found.
A member of Zizzi staff who answered the phone declined to comment.
Temporary Assistant Chief Constable Craig Holden said: "The pair, who we believe are known to each other, did not have any visible injuries and were taken to Salisbury District Hospital.
"This has not been declared as a counter terrorism incident and we would urge people not to speculate. However, I must emphasise that we retain an open mind and we will continue to review this position."
Garry Kasparov, a former world chess champion and critic of Vladimir Putin, was among those who drew comparisons with the death of Russian dissident Alexander Litvinenko in 2006.
But Igor Sutyagin, who was part of the same swap deal as Skripal and is now a research fellow at RUSI, urged caution.
He told the Associated Press: "There are lots of former security officers that deserted to the West. It is necessary to balance this information."
A spokesman for the Russian Embassy in the UK, when asked for comment on the incident, said: "Neither relatives nor legal representatives of the said person, nor the British authorities have addressed the embassy in this regard."
Salisbury District Hospital declared a major incident but told patients to attend appointments as normal unless advised otherwise.
Freya Church, who saw the couple on the bench, told the BBC they "looked so out of it".
She said: "He was doing some strange hand movements, looking up to the sky.
"It looked like they had been taking something quite strong."
A spokesman for Public Health England (PHE) said anyone exposed to the unknown substance had been decontaminated "as is standard practice in situations like this".
Among the Russian agents deported from America as part of the spy swap deal was Manhattan socialite and diplomat's daughter Anna Chapman, who was married to a British man and lived in London for several years.
While the incident in Salisbury is shrouded in mystery, it comes at a time of major tension in UK-Russian relations.
A report from the Commons Foreign Affairs committee last year describing the relationship between the two countries as being at "its most strained point since the end of the Cold War".
And in evidence to the Commons Intelligence and Security Committee, MI6 described the Russian state as "formidable adversaries".
In 2006, Mr Litvinenko died in London after drinking tea laced with radioactive polonium-210.
A public inquiry concluded in 2016 that the killing of Mr Litvinenko, an outspoken critic of Vladimir Putin, had "probably" been carried out with the approval of the Russian president.