LONDON — Britain’s Parliament grabbed control Monday of the government’s efforts to leave the European Union, challenging the country’s political traditions and inflicting on Prime Minister Theresa May a rebuke not suffered by any recent predecessor.

By stepping into the process known as Brexit and trying to define an alternative path, lawmakers could create a constitutional showdown in Britain, where the government normally controls the agenda in Parliament, especially on its most pressing issues.

Parliament passed an amendment giving itself the power to vote on alternatives to the government’s Brexit plan. Its attempt to take control of the process came as Mrs. May prepared for a last-ditch effort to persuade lawmakers to support her withdrawal plan, which has already been rejected twice by huge margins.

On Monday she admitted that there was “not sufficient support” to make another quick attempt to push it through, though she might try again on Thursday.