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Tonbridge and Malling MP Tom Tugendhat has suggested there could be a way for the UK to leave the EU within the next 10 days.
The MP, who chairs the cross-party Foreign Affairs select committee, has sketched out a possible way Brexit could happen ahead of the October 31 deadline and avoid the threat of a vote of no-confidence.
He tweeted the idea, emphasising he was not arguing for it to happen, but that it could be a way to outflank the government's opponents.
He asked what the odds could be on a surprise early Brexit in which the UK would unilaterally leave by August 24, followed by an election and a referendum in Northern Ireland on a backstop.
The MP was among 20 Conservatives - including the former business minister and Tunbridge Wells MP Greg Clark - who wrote to Boris Johnson accusing him of setting the bar too high in negotiations with the EU to have a hope of getting changes to a deal.
The letter, headed by the former Chancellor Philip Hammond, accused the PM of going back on campaign pledges not to leave with no deal in place.
It has been seen as further evidence of growing rift within the Conservative party over Brexit with the likelihood of a vote of no confidence growing ahead of the October 31 deadline.
Meanwhile, Liberal Democrat South East MEP Anthony Hook says he endorses Mr Hammond's criticism: "He is completely correct to say no deal would be a betrayal of the 2016 referendum result.
"We've gone from promises of extra money for the NHS and trade deals being sewn up by lunchtime to whether shop shelves will be bare or if we'll run out of medicines.
"I've been talking with the Port of Dover and the Channel Tunnel operators who tell me traffic gridlock in Kent is a very real possibility.
"It's perfectly clear nobody voted to die in the back of an ambulance unable to get to hospital."
All of this comes as Jeremy Corbyn wants to form a caretaker government in attempt to stop no-deal Brexit.