Jeremy Corbyn has called for Brexit to be delayed until after March 2019 if it allows the Government to secure “a better deal”.

The Labour leader surprised MPs by giving his personal backing to “dropping the unnecessary exit date deadline” from the EU Withdrawal Bill, ahead of a crunch vote next week.

Speaking in the Commons – as Tory MPs praised Theresa May for last week’s Brussels deal to move the exit talks onto trade – Mr Corbyn said she had only “scraped through”.

He pointed out that the Government had intended to conclude phase one of the negotiations two months ago and that the agreement reached on Friday was “fudged”.

“Has this experience given the Prime Minister reason to consider dropping the unnecessary exit date deadline of the 29 March 2019 from the EU Withdrawal Bill,” Mr Corbyn asked.

He added: “I’m sure the whole House, and probably the whole country, would rather get the best possible deal a little bit later if that meant a better deal for peoples’ jobs and the economy.”

The comments were seized on by the Prime Minister as fresh evidence that Labour could not be trusted to stand by its commitment to “uphold the referendum”.

She told MPs: “We’re leaving the European Union on that date. That is what the British people voted for and that is what this Government is going to put in place.”

The clash comes ahead of a crucial vote next week in which pro-EU Tory MPs will join forces with opposition parties to try to remove the Brexit date and time from the bill.

The Prime Minister has made it a show of strength – but could yet be forced to back down if more Conservative MPs join the revolt, fearing it will box the Government in.

The controversy is closely linked to a vote on Wednesday to give MPs a binding “meaningful vote” on the final Brexit deal. Both centre on the power of MPs to delay departure, if no satisfactory trade deal has been achieved.

Mr Corbyn’s support is further evidence of Labour softening its stance, after Keir Starmer, the party’s Brexit Secretary, said it wanted to “stay aligned” to the EU single market and customs union.

Meanwhile, the statement saw the Prime Minister praised by both pro and anti-EU Conservative MPs, following Friday’s agreement to move the Brexit talks onto trade and a transitional deal.

The former chancellor and pro-Remain MP Ken Clarke said: “I congratulate the Prime Minister on her triumph,” – while Nicky Morgan, another ex-Cabinet Brexit critic, said “thank you” on behalf of EU citizens.

But most hard-Brexit supporting Conservatives also held their fire, despite No 10 confirming the guarantee of “full alignment” of regulations, if necessary, to avoid a hard Irish border, would have legal force.

Only the Conservative MP Philip Davies spoke out, saying: “Why are we paying tens of billions of pounds, that are not legally enforceable, to the EU when she is continuing a policy of austerity at home?”

The Prime Minister confirmed the size of the divorce bill, telling MPs: “The calculations currently say that that would be £35bn to £39bn.”

But she calmed most backbench unease by insisting the UK would not pay the money unless agreement is also reached on a “future partnership” covering trade.

“This offer is on the table in the context of us agreeing the partnership for the future, agreeing the next stage and agreeing the partnership for the future. If we don’t agree that partnership, then this offer is off the table,” the Prime Minister warned Brussels.

This is strongly disputed, with critics pointing to paragraph 96 of last Friday’s text, stating the UK’s commitment to the agreement even if there is only a “framework” for a trade deal.

But, when this was pointed out, Ms May replied: “No, that is not my understanding.”

The warm welcome for the Prime Minister from her own MPs does not mean that the Conservative Party has ended its Brexit wars, but she has achieved a temporary ceasefire.

The battle is likely to resume as soon as next week, when the Cabinet debates its preferred “end state” – whether to remain close to the EU’s economic structures, or diverge and seek to deregulate.

That could bring some members into conflict with the Prime Minister’s concession of “full alignment” with EU regulations, if necessary to avoid customs checks and posts at the Irish border.