Theresa May has dramatically torn up her Brexit strategy, paving the way for a softer withdrawal in a bid to secure Jeremy Corbyn’s backing to pull Britain out of the EU.

The prime minister confirmed the UK would seek a further short delay to Brexit beyond 12 April in a Downing Street statement that infuriated Eurosceptic Tories.

Government insiders believe the two big parties’ positions on future customs arrangements are not so far apart and could form the basis of a new deal.

No 10 aides said the PM would approach talks in a “constructive spirit”, but within minutes other sources suggested discussions would simply be used to recapture control of the Brexit agenda as MPs come close to forcing an outcome on the government.

Mr Corbyn agreed to a meeting, possibly set to take place as early as Wednesday, saying he recognised his responsibility “to represent the people that supported Labour” at the last election.

Ms May’s move came after a marathon seven-hour cabinet during which ministers had mobiles taken off them to prevent clandestine briefing to the press ahead of the prime minister’s statement.

Brexiteer ministers who have said they would quit if the PM pursued a customs union were yet to resign last night with the final Brexit outcome still unclear.

In her statement Ms May said: “Today I am taking action to break the logjam.

Opposing protesters flock to parliament on would be date of Brexit Show all 30 1 /30 Opposing protesters flock to parliament on would be date of Brexit Opposing protesters flock to parliament on would be date of Brexit Pro-Brexit leave the European Union supporters attend a rally in Parliament Square after the final leg of the "March to Leave" in London AP Opposing protesters flock to parliament on would be date of Brexit The protest march which started on March 16 in Sunderland, north east England, finished on what was the original date for Brexit to happen before the recent extension Reuters Opposing protesters flock to parliament on would be date of Brexit A Brexit supporter holds up a poster during a rally after the final leg of the "March to Leave" in London, Friday, March 29, 2019. Pro-Brexit demonstrators were gathering in central London on the day that Britain was originally scheduled to leave the European Union. (AP Photo/ Kirsty Wigglesworth) Kirsty Wigglesworth AP Opposing protesters flock to parliament on would be date of Brexit A pro-Brexit protester holds a sign next to a statue of Winston Churchill at the March to Leave demonstration in London, Britain March 29, 2019. REUTERS/Toby Melville TOBY MELVILLE Reuters Opposing protesters flock to parliament on would be date of Brexit Brexit demonstrators in Parliament Square in Westminster, London. PRESS ASSOCIATION Photo. Picture date: Friday March 29, 2019. See PA story POLITICS Brexit. Photo credit should read: Jonathan Brady/PA Wire Jonathan Brady PA Opposing protesters flock to parliament on would be date of Brexit Pro-Brexit protesters hold signs and wave flags at the March to Leave demonstration in London, Britain March 29, 2019. REUTERS/Toby Melville TOBY MELVILLE Reuters Opposing protesters flock to parliament on would be date of Brexit epa07471421 Pro-Brexit protesters gather outside of the Parliament for Nigel Farage's 'March to Leave' in London, Britain, 29 March 2019. MPs rejected Prime Minister's May EU withdrawal agreement earlier in the day. EPA/NEIL HALL NEIL HALL EPA Opposing protesters flock to parliament on would be date of Brexit A Brexit supporter sips a can of Stella in protests outside of the Houses of Parliament AFP/Getty Opposing protesters flock to parliament on would be date of Brexit Dedicated anti-Brexit campaigner Steve Bray and likewise pro-Brexit campaigner Joseph Afrane go head to head near the Houses of Parliament AFP/Getty Opposing protesters flock to parliament on would be date of Brexit A pro-Brexit marching band in Parliament Square Getty Opposing protesters flock to parliament on would be date of Brexit Remain supporters wave EU flags from a bus in Parliament Square PA Opposing protesters flock to parliament on would be date of Brexit A Brexit supporter shouts slogans outside parliament EPA Opposing protesters flock to parliament on would be date of Brexit A Brexit supporter protests outside parliament Reuters Opposing protesters flock to parliament on would be date of Brexit A Brexit supporter protests outside of the Houses of Parliament Getty Opposing protesters flock to parliament on would be date of Brexit Brexit supporters protest outside of the Houses of Parliament REUTERS Opposing protesters flock to parliament on would be date of Brexit A pro-Brexit flag is waved in Parliament Square AP Opposing protesters flock to parliament on would be date of Brexit The March to Leave nears the Houses of Parliament Reuters Opposing protesters flock to parliament on would be date of Brexit A Brexit protester holds a sign outside parliament EPA Opposing protesters flock to parliament on would be date of Brexit Brexit supporters carry the coffin of democracy AFP/Getty Opposing protesters flock to parliament on would be date of Brexit Brexit supporters march outside parliament AFP/Getty Opposing protesters flock to parliament on would be date of Brexit Brexit supporters take part in the March to Leave protest in London PA Opposing protesters flock to parliament on would be date of Brexit Brexit supporters protest outside parliament AFP/Getty Opposing protesters flock to parliament on would be date of Brexit A Brexit supporter holds a sign outside the Houses of Parliament Getty Opposing protesters flock to parliament on would be date of Brexit A man holds satirical paintings of politicians Reuters Opposing protesters flock to parliament on would be date of Brexit An pro-Brexit float on the March to Leave march in London Reuters Opposing protesters flock to parliament on would be date of Brexit Far-right activist Tommy Robinson addresses protesters outside the Houses of Parliament Getty Opposing protesters flock to parliament on would be date of Brexit A Brexit supporter outside the Houses of Parliament Reuters Opposing protesters flock to parliament on would be date of Brexit A Tommy Robinson supporter arrives at the Houses of Parliament Getty Opposing protesters flock to parliament on would be date of Brexit A jogger gestures rudely at a Brexit supporter outside of the Houses of Parliament AFP/Getty Opposing protesters flock to parliament on would be date of Brexit A Brexit supporter outside the Houses of Parliament PA

“I am offering to sit down with the leader of the opposition and try to agree a plan – that we would both stick to – to ensure that we leave the European Union and that we do so with a deal.”

The prime minister said the idea would be to agree on a joint approach both she and Mr Corbyn can back and if not, put forward several different options for future relations with the EU for the Commons to vote on.

We recognise that she has made a move. I recognise my responsibility to represent the people that supported Labour in the last election and the people who didn’t support Labour, but nevertheless want certainty and security for their own future Labour leader Jeremy Corbyn

The Independent understands Ms May would be likely to bring back her own previously defeated deal as one of the options at that point, if initial talks with Mr Corbyn fail.

The prime minister said she would “abide by the decision” of the Commons and that Mr Corbyn would have to as well for the approach to work.

The Labour leader responded: “We recognise that she has made a move.

“I recognise my responsibility to represent the people that supported Labour in the last election and the people who didn’t support Labour, but nevertheless want certainty and security for their own future and that’s the basis on which we will meet her and we will have those discussions.”

Jeremy Corbyn says he is 'very happy' to meet Theresa May after her latest Brexit announcement

The PM’s aides would not rule out that discussions could include a customs union or even giving the British public a Final Say referendum on Brexit, although they pointed to the PM’s previously stated views.

The government’s current plan for future relations include many facets of a customs unions, while Mr Corbyn’s approach calls for “a customs union” but one that would give the UK greater freedoms than Britain’s existing EU membership.

The Conservative Party is already in turmoil, with one MP quitting on Monday claiming the cabinet is “cowardly and selfish” – but the idea that Ms May could strike a deal with Labour will probably push the Tories to the brink of a major rupture.

Boris Johnson said: “It is very disappointing that the cabinet has decided to entrust the final handling of Brexit to Jeremy Corbyn and the Labour Party.

“It now seems all too likely that British trade policy and key law making powers will be handed over to Brussels – with no say for the UK.”

He said it would be “ridiculous” if the UK were forced to contest European elections as a result of the further delay, adding: “I can under no circumstances vote for a deal involving a customs union as I believe that does not deliver on the referendum.”

Emmanuel Macron says he is 'open' to long Brexit delay for referendum, general election, or softer deal

Ms May delivered her statement while the Brexit-backing European Research Group (ERG) met, with its members watching her on television and one reporting, “it did not go down well”.

Chair of the ERG Jacob Rees-Mogg attacked Ms May for working with “a known Marxist”, and when asked if he could back a deal struck with Mr Corbyn, he said: “Well, I wouldn’t hold your breath – I’m not a Marxist in case you hadn’t noticed.”

He added: “What was announced today was an attempt to overturn the referendum that wanted a clear Brexit, to do a deal with a socialist who doesn’t want Brexit and is not in line with the Conservative Party’s manifesto commitments or with the referendum.”

But one minister told The Independent that the move was about ensuring that a cross-party move by MPs, led by ex-Tory minister Sir Oliver Letwin and Labour’s Yvette Cooper, to impose an outcome on the government is superseded, with the Commons looking to vote on its own options again soon.

Cabinet ministers were called to Downing street at 9.30am on Tuesday for a stormy meeting, one without civil servants, to discuss the way ahead.

MP Steve Baker calls himself 'Brexit hard man Steve Baker' in Sky News interview

It lasted until 2pm, with ministers eating sandwiches for lunch, before going into a formal government cabinet until 5.30pm.

Ms May’s aides were clear that there was little support for a general election, but would not confirm there had been unanimous backing for her suggested approach, with The Independent hearing differing reports of the level of opposition.

One suggested that the majority for an extension in cabinet was 17 to four, with only two of the 17 calling for a long one and two further making a point about backing a short one.

The four ministers who opposed it were Liz Truss, Chris Grayling, Gavin Williamson and Penny Mordaunt, according to the source. Some other ministers were not explicit in their view.