Theresa May plans to clinch a final Brexit deal just days before the UK crashes out of the EU, reports claim.

The Sun on Sunday’s political editor David Wooding says the prime minister will look to secure concessions to her withdrawal agreement at a summit of EU leaders on 22 March with a final deal put to the Commons the following Tuesday, just three days before the UK formally leaves the bloc on 29 March.

“Downing Street hope the tight margin will win over enough MPs to back a freshly-tweaked deal” says Wooding, however, it represents a high-stakes game of brinkmanship which dramatically increases the chance of an accidental no-deal Brexit.

Former government chief whip Mark Harper has urged MPs to “hold their nerve right up to the wire” to give the prime minister “a fighting chance to secure the necessary changes to the withdrawal agreement to get Parliament’s approval”.

Meanwhile, a senior government source said: “It’s a tight landing zone – but it’s a landing zone nevertheless. If we can get our timing right, we’ll touch down in time.”

Carolyn Fairbairn, head of the Confederation British Industry, told Sky News the prospect of the UK leaving the EU without a deal has “gone up” as the possibility of a deal getting through parliament recedes.

The BBC reports that Theresa May will ask MPs on Wednesday for more time to get legally-binding changes to the controversial Northern Irish backstop, “which she believes will be enough to secure a majority in Parliament for her deal”.

However, Labour's shadow Brexit secretary, Sir Keir Starmer, says he believes the prime minister is “pretending to make progress” on this issue.

He told The Sunday Times he thought May’s real intention was to run the clock down until the final week before Brexit to offer MPs a “binary choice” between her deal and no deal.

“We shouldn’t be put in a position where the clock is run down and the prime minister says it’s either my deal or even worse. That isn’t right in terms of the respect for parliament,” said Starmer.

In a bid to stop a last-minute showdown, Labour will table an amendment this week to force a meaningful vote on Theresa May’s withdrawal deal by 26 February.

Reuters reports May’s opponents are expected to put forward a series of alternative approaches which will be voted upon, “although it is not clear yet whether any will have sufficient support to pass, and if they do, whether they will force the government to act”.

One option could see the idea of holding a second referendum voted on in the Commons. The Observer reports that a new plan is being drawn up by a cross-party group of MPs to approve May’s Brexit deal “in return for guaranteeing another referendum.”

Politico says “May and her most senior advisers have long waited for the chance to put a second referendum to a vote in the House of Commons”.

In Brexit war-gaming sessions inside Number 10 Downing Street, removing a “People’s Vote” from the list of available options is a key staging post en route to MPs finally backing the prime minister’s deal, one senior government official told the news site.

An opinion poll for The Independent showed 53% of British voters would support a delay in Brexit, while 33% would back a no-deal Brexit even it that harmed the economy.