LONDON — When the world last focused full attention on Prime Minister Theresa May of Britain, she had returned from a “begging tour” in Europe with a Brexit extension she had hoped never to ask for and was fighting for her political life with her Conservative Party in open revolt.

She won the extension, to Oct. 31, but she is still fighting for her political life, this time against the embarrassing backdrop of a rising Brexit Party helmed by Nigel Farage that is easily outperforming Conservatives in most opinion polls.

All that seems to have led Mrs. May to take a last, desperate gamble, by holding a fourth — and, almost certainly, final — vote on a plan to leave the European Union that Parliament has rejected three times already. The vote seems set for the week beginning June 3, which is also when President Trump is scheduled to make a state visit to Britain.

Mrs. May has promised to stand aside if Parliament approves her plan, but she could face the exit gate anyway if Parliament were to reject it a fourth time.