LONDON (REUTERS) - Prime Minister Theresa May said on Tuesday (April 2) that she would ask for another Brexit delay to sit down with the opposition Labour leader, a last-ditch gambit to break the deadlock over Britain's exit that enraged many in her febrile party.

Nearly three years since Britain voted to leave the European Union in a shock referendum result, it is still unclear how, when or if it will ever indeed quit the European club it first joined in 1973.

In a hastily arranged statement from her Downing Street office after spending seven hours chairing Cabinet meetings on how to plot a way out of the Brexit maze, Mrs May said she was seeking another short extension to Brexit beyond April 12.

Mrs May's move offers the prospect of keeping Britain much more closely tied to the EU economically after Brexit - though it could also rip her Conservative Party apart, as half her lawmakers want a decisive split with the bloc.

"I am offering to sit down with the leader of the opposition and to 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," she said.

"We will need a further extension of Article 50, one that is as short as possible and which ends when we pass a deal. We need to be clear what such an extension is for - to ensure we leave in a timely and orderly way."

Labour leader Jeremy Corbyn said he would be "very happy" to meet Mrs May and that he would set no limits ahead of the talks, while reiterating that his party aimed to keep a customs union with the EU, access for Britain to its single market and protections for workers.

He added that he would hold a vote of no-confidence in the government in reserve if any eventual deal still failed to achieve a majority in Parliament. "Our responsibility as the opposition is to make sure that we don't crash out (in the absence of a deal)," he said in a broadcast interview.

Preserving close relationships with the EU is anathema to much of the increasingly eurosceptic Conservative Party.

Indeed, Brexit-backing Conservatives were livid over Mrs May's gesture to Labour.

"This is a deeply unsatisfactory approach, it is not in the interests of the country, it fails to deliver on the referendum result and history doesn't bode well for it," Mr Jacob Rees-Mogg, a prominent Brexiter, told reporters following a meeting of the party's hardline eurosceptic parliamentary group.

"You do find that leaders who decide to go with the opposition rather than their own party do find that their party do not tamely follow," he said, citing the example of a 19th century British political split over Corn Laws.

Mr Boris Johnson, the face of the 2016 Brexit campaign, said a compromise with Labour would betray the referendum, asserting that the world's fifth biggest economy could be outside the EU but still subject to EU rules.

LAST GAMBLE?

Any plan, Mrs May said, would have to include the current Withdrawal Agreement that she agreed with the EU in November and which the bloc says it will not reopen.

She said that if she could not agree a unified approach with Mr Corbyn, a veteran socialist who voted against joining the bloc in 1975, then the government would agree a number of options on the future relationship.

Then, she said, the government would put them before the House of Commons in a series of votes.

"If we cannot agree on a single unified approach, then we would instead agree a number of options for the future relationship that we could put to the House in a series of votes to determine which course to pursue," Mrs May said.

"Crucially, the government stands ready to abide by the decision of the house."

Mrs May's move could cleave apart her Conservatives, who have been grappling with an internal schism over Europe for the past three decades. Over half of her lawmakers voted last week to go for a no-deal Brexit, to the dismay of British business.

"It seems to me that she wants to rely upon Labour votes to get this extension through," Mr David Jones, a Brexit-supporting former Conservative minister, told Reuters. "If she does that, then she is putting the future of the party in peril."

Mrs May said she wanted the Withdrawal Agreement Bill to be passed before May 22 so that Britain does not have to take part in elections that month to the European Parliament.

Her own divorce deal with the EU has been resoundingly defeated three times by the Lower House of the British Parliament, which failed on Monday to find a majority of its own for any alternatives.

The impasse has already delayed Brexit for at least two weeks beyond the planned departure date of March 29, to 2200 GMT on April 12.

"This is a decisive moment in the story of these islands," Mrs May said. "But we can and must find the compromises that will deliver what the British people voted for."