The Labour Party said it was “disappointed” with the talks and claimed the Prime Minister was unwilling to change even the non-binding part of her Brexit deal on future trade with the EU to allow a customs union.

Meanwhile, Mrs May’s request for an extension of Article 50 until not later than 30 June looks set to be rejected in Brussels, with EU Council President Donald Tusk set to offer only a one-year delay.

Even a long extension could be rejected at Wednesday’s summit of EU leaders, with the governments of France, Spain and Belgium all ready to block any delay because they are not convinced the UK will be able to ratify a deal.

Prime Minister Theresa May. Picture: Jack Taylor/PA Wire

Following yesterday’s talks, shadow Brexit secretary Sir Keir Starmer said ministers were “not countenancing any changes” to the wording of the political declaration

“We’ve had two rounds of talks and so far, the government isn’t proposing any changes to the deal. In particular it’s not countenancing any changes to the actual wording of the political declaration.

“Now obviously that’s disappointing; compromise requires change. We want the talks to continue and we’ve written in those terms to the government, but we do need change if we’re going to compromise.”

But a Downing Street spokesman struck a more upbeat tone, saying: “We have made serious proposals in talks this week, and are prepared to pursue changes to the political declaration in order to deliver a deal that is acceptable to both sides.

“We are ready to hold further detailed discussions this weekend in order to seek any such changes in the run up to European Council on Wednesday.”

Responding to Labour’s statement, Nicola Sturgeon said that, in her own talks with the Prime Minister on Wednesday, Mrs May “refused to indicate any compromise she might make”.

“It is a bizarre approach from someone who made great play of wanting to find consensus - and has just wasted yet more time,” the First Minister posted on Twitter.

The SNP’s Westminster leader, Ian Blackford, said the Prime Minister now had to offer a referendum on Brexit. “It comes as little surprise that behind the rhetoric the Tory government has proved as intransigent and stubborn as ever, offering no meaningful steps in ending the Brexit chaos it has created,” he said.

“The clock is ticking down and with just a matter of days before the deadline to a catastrophic no-deal exit, it is clear that the only way to end the Brexit impasse is by bringing this back to the people in a fresh EU referendum – with remain on the ballot paper.”

Prisons minister Rory Stewart insisted there was “quite a lot of life” left in talks with Labour.

“I know that there are going to be tensions,” he said. “In truth the positions of the two parties are very, very close and where there’s good will it should be possible to get this done and get it done relatively quickly.”

He insisted that “of course we are prepared to compromise” on the political declaration.

Failure to reach even an outline agreement by early next weeks puts the UK’s request for any delay to Brexit in jeopardy.

France’s Europe minister Amelie de Montchalin warned yesterday that an extension would not be granted automatically.

It would require the UK to put forward a proposal with “clear and credible political backing” and “in the absence of such a plan, we would have to acknowledge that the UK chose to leave the EU in a disorderly manner”.

The governments of Belgium and Spain are also thought to have taken a hard line on an extension when EU ambassadors met in Brussels yesterday.

The Prime Minister wrote to Mr Tusk requesting a delay until 30 June, with an option to leave earlier if she can get a Brexit deal through Parliament.

Mrs May said she will seek to secure ratification of the deal before European elections on 23 May, but conceded that the government would make “responsible preparations” for the UK to take part in the polls.

EU sources said the EU Council President is recommending a longer postponement of one year, with a break clause in the case of earlier ratification, in a so-called “flextension” deal.

Irish premier Leo Varadkar said a longer delay to Brexit “might make more sense” than the UK seeking “rolling extensions where there is an extension every couple of weeks because that just adds to the uncertainty”.

Prominent Brexiteer Jacob Rees-Mogg suggested the UK should retaliate any long extension by using its continued membership to block moves towards closer EU integration. “If a long extension leaves us stuck in the EU we should be as difficult as possible,” he tweeted.

Brexit: Theresa May facing a battle to secure her latest delay