LONDON — Britain’s prime minister, Theresa May, on Tuesday promised greater control for Parliament over withdrawal from the European Union, after a threatened rebellion by lawmakers forced her into a new and potentially significant retreat in the country’s troubled exit from the bloc.

The day began on an ominous note with the resignation of one of Mrs. May’s ministers over her plans for withdrawal, known as Brexit, and got steadily worse for the prime minister when some of her rebel lawmakers combined with opposition parties, posing the threat of a damaging defeat.

The vote concerned an amendment that had been added by the House of Lords to Mrs. May’s main Brexit legislation. The amendment would have given lawmakers more control over the process by, among other things, avoiding a last-minute, take-it-or-leave-it vote on whatever package the government negotiated with Brussels.

Mrs. May had appealed to lawmakers not to support the amendment, arguing that it would weaken her negotiating hand with the European Union. Ultimately, they were placated by promises of a timely vote and adherence to some of the technical guarantees demanded by a Conservative rebel, Dominic Grieve, about what happens if a Brexit deal proves unacceptable to Parliament.