LONDON — Prime Minister Theresa May of Britain has announced that she will step down as the Conservative Party leader on June 7, bringing into the open a party leadership struggle that has been underway on the sidelines for months.

But deep divisions within the party and the nation over Britain’s withdrawal from the European Union proved fatal to Mrs. May’s leadership, and it is not clear that a successor would fare any better. The race is already shaping up to be a crowded one, with near daily announcements from Conservative Party lawmakers throwing their hats into the ring.

Anyone seeking the job has to be nominated by two members of Parliament. If there is only one candidate, he or she automatically becomes the new leader. If there are more than two, lawmakers vote among themselves to narrow the field to two candidates, who then are put to a vote by the 120,000 mostly white, mostly aging Conservative Party members. The party said it expected to begin the nomination process in the week of June 10, after Mrs. May steps aside, and to complete the process by the end of July.