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Britain's exit on March 29 next year has been plunged into crisis by parliamentary opposition to the divorce deal she struck with the EU last month, which has opened up possibilities including a delay to Brexit or even another referendum on membership.
May on Monday cancelled a parliamentary vote on the deal, which is designed to maintain close future ties with the EU, after it became clear she would lose it.
Eurosceptic critics of the deal within her own party triggered a no-confidence vote in her leadership, hours after she returned from talks with European leaders aimed at winning additional assurances about her deal.
After two hours of voting in Committee Room 14 in the House of Commons on Wednesday, Graham Brady, chairman of the 1922 Committee of Conservative backbenchers, said 200 Conservative lawmakers had voted in support of May as leader, and 117 against.
May, who voted to remain in the EU in the 2016 referendum, had warned opponents of her withdrawal deal - struck after two years of negotiations - that if they toppled her, Brexit would be delayed or stopped.
Shortly before the vote, May sought to win over wavering lawmakers by promising to step down before the 2022 election.
Later she told media she would get on with her "renewed mission" of taking Britain out of the EU.
"Following this ballot, we now have to get on with the job of delivering Brexit for the British people and building a better future for this country," May said outside her Downing Street residence.
The Prime Minister said she would seek legal and political assurances from EU leaders on Thursday on the backstop arrangement over the border between EU member state Ireland and the British province of Northern Ireland.
Brexit is Britain's most significant political and economic decision since World War 2. Pro-Europeans fear the departure will weaken the West as it grapples with the US presidency of Donald Trump and growing assertiveness from Russia and China.
The outcome will shape Britain's $US2.8 trillion ($NZ4.08 trillion) economy, have far reaching consequences for UK unity and determine whether London keeps its place as one of the top two global financial centres
Supporters of Brexit admit there may be some short-term pain for Britain’s economy, but say it will prosper in the long term when cut free from the EU, which they cast as a failing German-dominated experiment in European integration.
May, the 62-year-old daughter of a Church of England pastor, won the top job in the turmoil that followed the 2016 EU referendum called by then Prime Minister David Cameron. She promised to implement Brexit, while keeping close ties to the bloc, to heal a divided nation.
A bitter division over Europe in the Conservatives helped bring about the downfall of all three previous Conservative premiers - Cameron, John Major and Margaret Thatcher.
May, who voted to remain in the EU at a 2016 referendum, told opponents of her EU withdrawal deal - struck after two years of negotiations - that if they toppled her, then Brexit would be delayed or stopped.
Pro-Brexit hardliners in her party say May has betrayed the people's vote in negotiations, while other critics say she struck a deal that is the worst of all worlds - out of the EU but with no say over rules it has to abide by.
"Theresa May's plan would bring down the government if carried forward," lawmakers Jacob Rees-Mogg and Steve Baker said in a statement. "Conservatives must now answer whether they wish to draw ever closer to an election under Mrs May’s leadership. In the national interest, she must go."
The EU's top court ruled on Monday that Britain could cancel its Article 50 notice to leave without permission from other members and without losing privileges.
But if May's deal fails in parliament and Brexit is not delayed, then Britain could be heading towards a disorderly exit that investors fear will clog the arteries of trade, dislocate supply chains and roil markets.
"We are working hard to make sure we get an orderly Brexit," said German Chancellor Angela Merkel, the EU's most powerful leader.