LONDON — Time is not on Britain’s side as the clock ticks down to its scheduled March 29 exit from the European Union and its politicians remain paralyzed over how the country should leave.

But on Thursday, decision day was delayed once again when a critical debate and vote in Parliament that could help break the deadlock was put back until Jan. 29.

Delay has been a frequent tactic of Prime Minister Theresa May, who has gambled that the pressure of a looming deadline for departure would persuade lawmakers to accept her plan for withdrawal, or Brexit.

That hit the rocks this week when her proposals suffered a crushing defeat in Parliament, leaving the country in limbo and suggesting that Mrs. May would have to redraw her plans or surrender leadership to lawmakers.