LONDON — Her cabinet is split and her party is at war, but Britain’s prime minister, Theresa May, recently found time to get out and about, and says she heard a clear message from a weary public.

“They want to see this resolved,” Mrs. May told Parliament, referring to the tortuous, tedious, yet momentous task of withdrawing from the European Union, a process known as Brexit.

If so, the British are in for a disappointment. Not only is the Brexit process really just starting, in some respects it might never end.

On Tuesday, lawmakers are scheduled to vote on Mrs. May’s two-part plan for Britain’s departure: a legally binding agreement laying down divorce terms from the bloc, and a much vaguer declaration on future ties. If they defeat it, as many expect, they will be back to square one and, in all likelihood, pleading for an extension from the European Union that could last anything from a couple of months to a couple of years.