Foreign Secretary Boris Johnson even suggested England could pull out of the 2018 FIFA World Cup in Russia if it were shown to be behind the incident.
Sergei Skripal was a former colonel in Russian military intelligence who spied for Britain and moved there in a spy swap in 2010.
He was found outside a shopping centre along with his daughter, Yulia, in the southwestern English city of Salisbury on Sunday.
The pair were treated for "suspected exposure to an unknown substance" and are in a critical condition in a local hospital, police said in a statement.
Mr Johnson told the House of Commons that it was too soon to establish the cause of the "disturbing" incident, which caused a major security alert in the normally quiet city.
But he noted "echoes" of the 2006 poisoning in London of Kremlin critic Alexander Litvinenko. A British inquiry ruled that attack was likely ordered by Russian President Vladimir Putin.
"Should evidence emerge that implies state responsibility, then Her Majesty's government will respond appropriately and robustly," Mr Johnson said.
"Though I am not now pointing fingers, I say to governments around the world that no attempt to take innocent life on UK soil will go either unsanctioned or unpunished."
Mr Johnson went on however to refer indirectly to suspected Russian involvement. If that is confirmed, he said, "it will be difficult to see how UK representation at the World Cup can go ahead".
Government briefed
Britain's National Security Council discussed the Skripal affair at a meeting on Wednesday, where Prime Minister Theresa May, Mr Johnson and senior ministers were updated on the ongoing investigation, according to a government spokesman.
The incident has not been linked to terror but Britain's national counter-terrorism unit took control of the case Tuesday, saying it had the specialist expertise to deal with such "unusual circumstances".
A cordon remained in place Tuesday where Mr Skripal, 66, and his 33-year-old daughter were found, while a restaurant on a street nearby, Zizzi, was also closed.
Police earlier revealed a number of emergency services personnel required medical assessment after the incident, but stressed there was no risk to public health
UK-Russia tensions
The murder of Mr Litvinenko, an ex-Russian spy killed by radioactive polonium in his tea, led to a major diplomatic split between London and Moscow.
A British inquiry ruled in 2016 Mr Putin "probably approved" the killing and identified two Russians, Andrei Lugovoi and Dmitri Kovtun, as the prime suspects.
Many MPs warned on Tuesday of the current threat posed by Moscow, citing its actions in Ukraine and cyber-attacks. There are also tensions over Russia's role in the Syrian conflict.
The chairman of the House of Commons foreign affairs committee, Tom Tugendhat, said the early evidence pointed to Russia's involvement in the Salisbury incident.
"It is too early to say whether it is certain or not, but it certainly bears all the hallmarks of a Russian attack," he said.
Mr Putin's spokesman Dmitry Peskov said earlier on Tuesday Russia had no information about the cause of the "tragic situation".
He said London had not made any requests for assistance in the investigation, but added: "Moscow is always ready for cooperation."
Mr Lugovoi, who is an MP in the Russian parliament, dismissed suspicions of poisoning as British "phobias", saying Mr Skripal was of no interest to the authorities.
'Deja vu'
Mr Skripal was sentenced to 13 years in jail in Russia in 2006 for betraying Russian intelligence agents to Britain's MI6 secret service.
But he was pardoned before being flown to Britain as part of a high-profile spy swap involving Russia and the United States in 2010.
Igor Sutyagin, who also went to Britain in the swap, said he could not understand why Mr Skripal would be targeted.
"He confessed, was amnestied and had served part of his sentence," he told Radio Free Europe.
However, Mr Litvinenko's widow, Marina, told The Times newspaper the case brought on a "kind of deja vu".
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