LONDON — Prime Minister Theresa May of Britain expelled 23 Russian diplomats on Wednesday over the poisoning of a former Russian spy on British soil, raising tensions between the two countries to a level not seen since the heights of the Cold War. She vowed to crack down on Russian spies, corrupt elites and ill-gotten wealth in Britain.

Her statement to Parliament came after Moscow rejected a British deadline for Russia to explain itself over this month’s attack on the former spy, Sergei V. Skripal, and his daughter.

The two countries have engaged in a worsening clash in recent days, with Britain widening an investigation into the incident and courting friends and allies to increase pressure on Russia, while Moscow has threatened to retaliate over any punitive action.

The strident remarks from the British prime minister were a marked departure from the norm for a leader who has faced a litany of domestic and international issues. Mrs. May’s government is consumed with Britain’s withdrawal from the European Union, a complex negotiation that it appears to be struggling with. And its closest international ally, the United States, is led by a president who has appeared reluctant to openly criticize Russia.