British MPs are attempting to overturn centuries of constitutional convention in a bid to take control of Brexit from Theresa May’s government and prevent a no-deal departure from Europe.

Prime Minister May is battling to break a deadlock after last week’s crushing defeat of her two-year attempt to forge an orderly divorce from the European Union, raising the prospect of an exit without a deal.

The opposition Labour Party on Thursday morning (Australian time) said it is likely to support an amendment proposed by MP Yvette Cooper that could result in Ms May being given until February 26 to get a deal approved by parliament or face a delayed Brexit.

The second most powerful figure in the Labour Party, John McDonnell, told the BBC the amendment was sensible and Labour was “highly likely” to back it.

At least nine Conservative MPs have also publicly said they will support it, suggesting it has a strong chance of passing.

The possible outcomes for the world’s fifth largest economy still include a no-deal Brexit, a last-minute deal, a delay or a snap election.

But the EU cautioned that no-deal was still the default scenario until London proposed something else.

“Preparing for a no-deal scenario is more important now than ever, even though I still hope that we can avoid this scenario,” EU Brexit negotiator Michel Barnier said in Brussels.

May has said thwarting Brexit would threaten social cohesion by undermining faith in democracy, while police have said the “febrile” atmosphere could be exploited by far-right extremists.

Another alternative is that May gets enough concessions from the EU to win over rebels in her Conservative Party as well as the Northern Irish party that props up her minority government.

Some said they could be won over if May secures concessions on the so-called Northern Irish backstop, an insurance policy to keep the border open between the British province and Ireland if a future trade deal falls short.

Parliament will vote on January 29 on different options put forward by MPs, potentially opening a way out of the stalemate.

If Cooper’s amendment is passed, it would effectively give parliament the power to set May a deadline of February 26 to get a deal through parliament.

If May fails, parliament would be given a vote on asking the EU for a postponement of the Article 50 deadline to prevent Britain leaving without a deal on March 29.

It proposes a nine-month extension, to December 31.

If Britain asked to delay its departure under Article 50, the other 27 EU members would need to unanimously approve such a move, something EU officials say would be likely to be granted.

“If this question is presented, they will have questions for the British government: What is it for, what is the purpose? For how long?” Barnier said.

-with AAP