May told parliament Britain would also freeze Russian state assets wherever there was evidence of a threat and downgrade its attendance at the soccer World Cup this summer.
Former spy Sergei Skripal, 66, and his daughter Yulia, 33, were found unconscious on a bench in the city of Salisbury on March 4 and remain in hospital in a critical condition.
May has said the pair was attacked with Novichok, a Soviet-era military-grade nerve agent.
She had asked Moscow to explain whether it was responsible for the attack or had lost control of stocks of the highly dangerous substance.
Russia has denied any involvement, and May told parliament Moscow had provided no credible explanation for the attack.