LONDON — Prime Minister Theresa May on Thursday suffered another significant defeat over Britain’s tortured exit from the European Union when a fragile truce within her Conservative Party collapsed, exposing fault lines in Parliament that are slowly widening as the deadline for leaving approaches.

By a margin of 303 to 258, lawmakers failed to support a motion endorsing the government’s battered strategy for Britain’s withdrawal, or Brexit, ignoring a warning from one minister that doing so could worsen Mrs. May’s chances of securing changes that could make her unpopular exit plan more palatable.

The latest defeat has no legal implications but is another in a numbing series of setbacks for Mrs. May, whose proposals for leaving the bloc were rejected by a historic margin last month and who needs concessions from Brussels before bringing a revised deal back to Parliament.

Mrs. May has assured European negotiators that she can get a majority for a revised Brexit plan, if they make some concessions. But this latest show of disunity from lawmakers, and rebellion from within her own party, appeared to confirm suspicions that legislators cannot coalesce around any plan they can accept.