LONDON — Prime Minister Theresa May of Britain survived a critical vote in Parliament on Tuesday that could have delayed Brexit, undermined her strategy for leaving the European Union and undercut the country’s constitutional protocol.
Mrs. May’s latest political escape came when lawmakers narrowly failed to approve an amendment giving Parliament the power to instruct her to seek a delay to avoid a disorderly, and possibly chaotic, exit that Britain faces on March 29 if there is no agreement.
However, she later lost a vote on a nonbinding amendment that said Britain should not leave the bloc without a deal, a sign of potential troubles ahead.
The stakes were high not just for the Brexit process but for the future of Britain’s democracy under its unwritten constitution, under which the government initiates legislation and Parliament amends it and votes on it.
Mrs. May had scathing words for the amendment, put forward by lawmakers Yvette Cooper, of the Labour Party, and Nick Boles, a Conservative, which she said seeks “to create and exploit mechanisms that allow Parliament to usurp the proper role of the executive.”
In her speech to Parliament before the vote, Mrs. May warned that “such actions would be unprecedented, and have far-reaching and long-term consequences for the way the United Kingdom is governed.”
As the vote approached, Mrs. May appealed to rebel lawmakers to hold their fire, promising them another chance to vote against a no-deal exit in February.
While Mrs. May survived to fight another day, her options are narrowing, and she faces an ever harder task in trying to reverse Parliament’s landslide rejection of her Brexit plan earlier this month.
In effect, she is back where she started before the amendment process. Her only card remains that, even if Parliament thoroughly dislikes her Brexit plan, Britain’s politicians remain divided and paralyzed over the alternatives.
Mrs. May, who has turned survival into a political art form, promised hard-line Brexit supporters in her own party that she could rework a carefully crafted, 585-page legal text, negotiated for almost two years, that European Union negotiators say cannot be reopened.
Until recently, she herself insisted that it would be impossible to renegotiate this withdrawal agreement. Mrs. May argued on Tuesday that, while challenging, it could be done.
She gained some needed support in the final vote of the night, when Parliament approved an amendment, drafted by a senior Conservative, Graham Brady, that voiced support for her strategy of reopening negotiations in search of “alternative arrangements” to the so-called Irish backstop plan, an insurance policy to keep goods flowing across the Irish border.
It was now clear, Mrs. May said after the amendment was passed, that “there is a route that can secure a substantial and sustainable majority in this house for leaving the E.U. with a deal.”
If European leaders stick to their word, Mrs. May is likely to have to settle for less fundamental, and more cosmetic, changes to her Brexit plan that went down to a seismic 230-vote defeat in Parliament earlier this month.
In a statement issued by the office of the European Council president, Donald Tusk, the bloc rejected Mrs. May’s latest strategy, saying that the Irish backstop “is part of the withdrawal agreement and the withdrawal agreement is not open for renegotiation.”
Mrs. May’s main hope remains that a Parliament that cannot agree on any other course will ultimately opt to support a modestly altered version of her deal for fear of a disastrous no-deal Brexit. Critics think she is in reality trying to run down the clock to present them with two bad options: her plan or no deal.
Ms. Cooper, one of the authors of the amendment that narrowly failed, said she had believed that Mrs. May would not allow Britain to leave without a deal because of the damage it could cause.
“I’ve always believed the prime minister would not let this happen,” she said. “She is not the sort of person who would want to make other people suffer because of her delays and mistakes. When I look into her eyes now, I am worried that has changed, because she is trapped.”
Other lawmakers spoke about the dangers of a no-deal Brexit, including Oliver Letwin, a senior Tory figure, who warned that were “terrible things” to happen, the Conservatives “will not be forgiven for many years.”
With the deadline pressing, Mrs. May’s next move will likely be to return to Brussels before going back to Parliament to try to convince lawmakers again.
But on Tuesday, Dominic Grieve, a pro-European Conservative lawmaker, said that Parliament was “mired in complete paralysis,” while one of his like-minded colleagues, Kenneth Clarke, said that Britain faced a constitutional crisis, with voters looking on at the political system “with something rather near to contempt.”