LONDON — Britain’s beleaguered prime minister, Theresa May, will face a no-confidence vote on Wednesday within her own Conservative Party, as lawmakers upset with her handling of Britain’s withdrawal from the European Union seek to topple her from power.

Graham Brady, the chairman of the backbench 1922 committee of Conservative lawmakers, announced Wednesday morning that he had received letters of protest from more than 48 Conservative members of Parliament, the number needed under party rules to trigger a vote on her leadership. He said the contest would take place Wednesday evening.

Mrs. May has been battered from multiple directions by her management of the European Union withdrawal, or Brexit. In particular, many hard-line Brexit supporters within her party believed she was not making a complete enough break with the bloc.

[What is Brexit? A simple guide to why it matters and what happens next.]

In recent days, she suffered two embarrassing setbacks in Parliament. Last week, the House of Commons voted her government in contempt of Parliament — the first time any prime minister had been censured in that way — for failing to release the advice her government’s lawyers had given on Brexit.