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British MPs signalled their opposition on Wednesday to leaving the European Union with a no deal on March 29, in another blow to Prime Minister Theresa May's authority.

The decision by parliament's lower House of Commons is largely symbolic as Britain is still on course to leave the EU in just over two weeks unless it can decide a new plan in agreement with Brussels.

Business leaders have warned that Britain is "staring down the precipice" as it faces the possibility of severing 46 years of UK-EU ties overnight, with the risk of an economic shock on both sides of the Channel.

And the manner in which MPs voted demonstrated once against the chaos in parliament over Brexit, including the lack of control that May has over events.

She had offered MPs a vote on a "no deal" option after they rejected for a second time on Tuesday the divorce terms she negotiated with the EU over many months.

Her proposal made clear that no deal was still the default option, but lawmakers decided instead to back an amendment rejecting "no deal" in all circumstances.

Wednesday's moves open the way for MPs to vote on Thursday on whether to ask the EU for a delay to Brexit - but Brussels has warned London must explain what it wants.

"Why would we prolong the negotiation? To do what?" EU chief negotiator Michel Barnier told the European Parliament in Strasbourg ahead of the vote in London.

May, her voice still hoarse, had warned MPs there were "hard choices" about what would come next.

"You can only take no deal off the table by doing one of two things: either revoke Article 50 (the Brexit process), which means betraying the vote of the referendum, or agree a deal," she said.

But her personal failure on Wednesday, when the rebel "no deal" amendment passed by 312 votes to 308, reveals how much her authority has suffered.

Subsequently, her government set out plans for a third parliamentary vote on her Brexit deal with the EU to be held by March 20.

In a proposal to be voted on by MPs on Thursday, the government states that if parliament has not approved the deal by that date it will ask the EU for an extension.

"This is a rudderless government in the face of a huge national crisis," opposition Labour leader Jeremy Corbyn said.

The pound took a brief knock after MPs rejected May's divorce deal for a second time on Tuesday, but rallied on hopes that MPs would now vote for a delay.

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