LONDON — Prime Minister Theresa May of Britain on Tuesday dangled the prospect of a second referendum on Brexit, in a last-ditch effort to win over lawmakers who have rejected three previous efforts to extract Britain from the European Union.

In a speech in London, Mrs. May outlined a plan to give Parliament a role in shaping her Brexit plan, but most attention focused on her mentioning the prospect of a second referendum, something she had previously ruled out.

Early reaction among Conservatives and Labour was not encouraging. The Labour leader, Jeremy Corbyn, said his party would not be supporting her legislation.

It was unclear how much of a concession Mrs. May was making. She was offering lawmakers a chance to vote on whether to have a referendum, rather than supporting one herself. And she was vague about what question or questions any referendum would pose.

She plans to hold a vote on her plan next month, and has promised to set a date after that for her departure after almost three troubled years in power.

The changes seemed designed to entice opposition Labour Party lawmakers to support her Brexit blueprint. These include the opportunity for Parliament to decide on whether to keep a type of customs union with Brussels, eliminating tariffs and reducing checks on goods at frontiers — a demand of Mr. Corbyn.

Parliament has previously voted against a second referendum, and Mrs. May said she still opposed the idea, making it unlikely that there would be sufficient support for it this time.

Nor has Parliament yet managed to coalesce around any plan to keep a customs union with the bloc.

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