Former double agent Sergei Skripal, 66, and his daughter Yulia, 33, were found unconscious on a bench in the genteel city of Salisbury on March 4 and remain in hospital in a critical condition.
She had given Moscow until midnight on Tuesday to explain how the Soviet-made Novichok nerve agent came to be deployed on the streets of Salisbury, saying either the Russian state was responsible or had lost control of a stock of the substance.
May also said London had notified the Organisation for the Prohibition of Chemical Weapons about the use of the nerve agent.
The Trump administration ramped up its criticisms of Russian Federation on Wednesday, with U.S. Ambassador to the United Nations Nikki Haley saying the U.S. believed Russian Federation was "responsible" for the attack on Skripal, an action she said was worthy of retaliation from the U.N. Security Council.
All four shared Britain's assessment that it was "highly likely" that Russia was responsible for the attack, and condemned Russia's failure to address the "legitimate" request by the United Kingdom government to explain whether and how a nerve agent developed under a Russian nerve agent programme could have gotten into third-party control.
Mrs May thanked emergency services in Salisbury and spoke to members of the public during her visit on Thursday.
Russian Federation denies being the source of the nerve agent used and has demanded Britain share samples collected by investigators.
The statement signals a more co-ordinated response from Britain's closest allies, but it lacked any details about specific measures the West would take if Russian Federation failed to comply.
The crisis has unravelled in the thick of Russia's presidential campaign, with Putin expected to win a fourth Kremlin term on Sunday.
European Union president Donald Tusk said Friday that the bloc would discuss the attack at a Brussels summit next week, adding it would send a "clear message".
Deputy Foreign Minister Sergei Ryabkov said Moscow was greeting the sanctions calmly, but he warned that Russian Federation had already started "to prepare a response".
The official military newspaper Krasnaya Zvezda quoted the former head of Russia's GRU military intelligence, Fyodor Ladygin, as denying his officers had been involved.
However British Foreign Secretary Boris Johnson told the BBC that Britain is "entirely in conformity" with OPCW procedures and is sending a sample of the nerve agent to the watchdog for examination.
Russia's ambassador in London, Alexander Yakovenko, said Mr Williamson's comments were part of a "shocking" political culture.
The war of words escalated after Mr Williamson suggested Russian Federation should "go away and shut up". "Prime Minister May's decision to expel the Russian diplomats is the level of response that many Americans have been craving from our own administration".
Meanwhile, Defence Secretary Gavin Williamson said Russian Federation should "go away and shut up".
Relations between Britain and Russian Federation have fallen to their lowest point since the Cold War, following the poisonings. "It threatens the security of us all".
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