LONDON — Against a backdrop of rising political acrimony, Theresa May, the British prime minister, warned critics on Sunday not to thwart her timetable for withdrawal from the European Union, as she prepared for a standoff with lawmakers that could prompt calls for an early general election here.

Mrs. May, who wants to start the formal process of leaving the bloc by the end of March, now has a serious fight on her hands, after several months of facing relatively little challenge over her plans for British withdrawal, known as “Brexit.”

Judges on Britain’s High Court ruled last week that she could not start exit negotiations by invoking Article 50 of the European Union’s treaty without first consulting Parliament, where the government’s majority is slim.

The government is appealing the case to the Supreme Court, but if it loses, and then finds itself constrained by lawmakers, the temptation to seek an early general election may become overwhelming for Mrs. May.