Sergei Skripal, 66, was granted refuge in the UK following a “spy swap” between the US and Russia in 2010.
He and a woman, 33, were found unconscious on a bench at a shopping centre in Salisbury on Sunday.
Zizzi restaurant in Salisbury has been closed by police “as a precaution”.
The substance has not been identified, but Public Health England said there was no known risk to the public’s health.
Wiltshire Police are investigating whether a crime has been committed. They said the pair had no visible injuries but had been found unconscious at the Maltings shopping centre.
They have declared a “major incident” and multiple agencies are investigating. They said it had not been declared as a counter-terrorism incident, but they were keeping an “open mind”.
Col Skripal, who is a retired Russian military intelligence officer, was jailed for 13 years by Russia in 2006 for spying for Britain.
He was convicted of passing the identities of Russian intelligence agents working undercover in Europe to the UK’s Secret Intelligence Service, MI6.
Russia said Col Skripal had been paid $100,000 for the information, which he had been supplying from the 1990s.
He was one of four prisoners released by Moscow in exchange for 10 US spies in 2010, as part of a swap. Col Skripal was later flown to the UK.
He and the woman, who police said were known to each other, are both in intensive care at Salisbury District Hospital.
A number of locations in the city centre were cordoned off and teams in full protective gear used hoses to decontaminate the street.
The hospital advised people to attend routine operations and outpatient appointments unless they were contacted. It said its A&E department was open but busy because of the weather.
Neighbours at Sergei Skripal’s home in Salisbury say police arrived around 17:00 GMT on Sunday and have been there ever since.
They said he was friendly and in recent years had lost his wife.
Eyewitness Freya Church told the BBC it looked like the two people had taken “something quite strong”.
She said: “On the bench there was a couple, an older guy and a younger girl. She was sort of leant in on him, it looked like she had passed out maybe.
“He was doing some strange hand movements, looking up to the sky…
“They looked so out of it I thought even if I did step in I wasn’t sure how I could help.”
The BBC’s security correspondent Gordon Corera said government officials were not commenting about events in Salisbury, but that the possibility of an unexplained substance being involved will draw comparisons with the 2006 poisoning of Alexander Litvinenko.
The Russian dissident died in London in 2006 after drinking tea laced with a radioactive substance.
A public inquiry concluded that his killing had probably been carried out with the approval of the Russian President, Vladimir Putin.
Gordon Corera said the first priority in this case would be understanding what the unknown substance was.
“But it’s also vital to establish for sure whether it was a deliberate poisoning because, if it was, that means the perpetrators are potentially still at large, perhaps still in the UK.”
The question, he said, was why this had happened.
“Is this someone who was targeted by Russian intelligence because they thought he was a traitor? Or is there some other reason, if indeed it was a deliberate poisoning?
“But, if it was a poisoning and the trail leads back to Moscow, then I think there will be real pressure on the British government to respond – and real questions asked about whether they did enough in the past to respond to previous incidents, to deter this kind of thing happening again.”
On the restaurant closure, police said Public Health England had reiterated their advice that there was no known risk to the public’s health.
“However, as a precaution they have advised that if you feel ill, contact the NHS on 111.
“If you feel your own or another’s health is significantly deteriorating, ring 999.”
What were the charges against Col Skripal?
Col Skripal was convicted of “high treason in the form of espionage” by Moscow’s military court in August 2006. He was stripped off all his titles and awards.
He was alleged by the Russian security service FSB to have begun working for the British secret services while serving in the army in the 1990s.
He had been passing information classified as state secrets and been paid for the work by MI6, the FSB claimed.
Col Skripal pleaded guilty at his trial and co-operated with investigators, reports said at the time.
BBC