LONDON—The British Parliament looks set to reject a proposed Brexit deal by a huge margin Tuesday, a defeat that will likely trigger a no-confidence vote in Prime Minister Theresa May’s government and force yet another round of frenetic negotiations with her European counterparts.

British lawmakers need to approve the Brexit agreement that Mrs. May crafted with the European Union for it to go into effect. But many lawmakers have balked at the deal in particular because of a clause that could see the U.K. indefinitely locked...