It comes after the two men suspected of targeting Sergei and Yulia Skripal with novichok have denied being Russian agents or having anything to do with the poisoning.
Alexander Petrov and Ruslan Boshirov told Russia Today (RT) they were only in Salisbury on 3 March as tourists to visit the cathedral and nearby Stonehenge.
In their first interview since being named as suspects by the British government they said they were victims of a “fantastical coincidence” and would like an apology from the real poisoners.
Responding to the interview, Theresa May’s spokesman said the suspects’ comments were “an insult” and “deeply offensive”.
“The lies and blatant fabrications in this interview given to a Russian state-sponsored TV station are an insult to the public’s intelligence,” he said.
“More importantly they are deeply offensive to the victims and loved ones of this horrific attack.”
Police officer Nick Bailey also came into contact with the nerve agent, along with Charlie Rowley and Dawn Sturgess soon after in nearby Amesbury. Ms Sturgess fell critically ill and died.
The prime minister’s spokesman told reporters police had set out “very clearly” the evidence against the two suspects and speaking about their denial of the claims, said “sadly, it is what we have come to expect”.
“They are wanted men and we have taken all steps to ensure they are apprehended and brought to justice in the UK if they ever again step foot outside Russia,” he added.
Petrov and Boshirov, who claimed they were not using pseudonyms, told RT their friends had told them to visit “this wonderful town, Salisbury, which has a famous cathedral and 123m spire, and is famous for its clock”.
They said they wanted to go to Stonehenge but were prevented from doing so because there was “muddy slush everywhere” so they got wet and went back to London an hour after arriving, as there was an intermittent weekend train service.
Southwestern Railway confirmed to Sky News there were engineering works that weekend and no direct trains from London to Salisbury, so they would have had to change at Basingstoke.
Petrov and Boshirov, who say they own a sports nutrition business, said “maybe” they approached former Russian spy Sergei Skripal’s house, “but we don’t know where it is located”.
Mr Skripal and his daughter, who are recovering at a safe house in the UK, were found slumped on a bench in Salisbury in March, having been poisoned with the nerve agent novichok.
The two Russian men, who say they are both about 40, were identified last week as suspects by the British government.
RT’s editor-in-chief said the two men approached her as they wanted to tell their story because they are now living in fear for their lives.
Mr Boshirov said: “When your life is turned upside down, you don’t know what to do and where to go.
“We’re afraid of going out, we fear for ourselves, our lives and lives of our loved ones.”
They confirmed they were the two men shown in CCTV pictures issued by the Metropolitan Police, saying they owned the clothes they were pictured in and even bought their shoes in England.
Salisbury MP John Glen said these statements were not credible and what they said did not match UK intelligence.
He added he was delighted that the Russians were able to see “the world class attractions Salisbury has to offer”.
A statement from English Heritage revealed Stonehenge – known as Old Sarum – was closed to the public from 1 March to 4 March this year because of the snow.
A Foreign Office spokesman said that the two men had been identified as the prime suspects and it was clear they were GRU officers who “used a devastatingly toxic, illegal chemical weapons on the streets of our country”.
“We have repeatedly asked Russia to account for what happened in Salisbury in March,” he added.
“Today – just as we have seen throughout – they have responded with obfuscation and lies.”
On Wednesday, Russian President Vladimir Putin said the two men had been identified by the Kremlin and insisted they were civilians and “not criminals”.
British intelligence found the novichok was stored in a fake Nina Ricci perfume bottle, but the two suspects said that would be a ridiculous way for them to transport poison, which they denied having, as it would be “silly for decent lads” to have women’s perfume.
Mr Boshirov said: “The customs are checking everything, they would have questions as to why men have women’s perfume in their luggage. We didn’t have it.”
The pair said they had travelled to Europe quite a lot for holidays and for business. They said they spent New Year’s Eve in Switzerland and have been to Vienna.
“We examine the market, look if there is something new – some biologically active additives, amino acids, vitamins, microelements,” the two said.
“We pick up the most necessary, come here and decide how to deliver the new products from this market here.”
The Russian embassy in the UK reacted as it has throughout the Skripal saga, by tweeting a picture of newspaper coverage of the Salisbury case, adding: “Insults and ultimatums do not qualify as questions.
“For its part, Russia has sent over 60 requests to UK, receiving no meaningful reply.”