Theresa May’s efforts to secure a Brexit deal by the end of March have suffered a serious setback after it emerged that UK and European Union negotiators were struggling to bridge the gap over the Irish border backstop in time for a November summit.

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The prime minister was forced to admit that “significant” issues remained despite talks that went on until the early hours of Monday morning. Unless there is dramatic progress by the end of Wednesday, the exit timetable will become increasingly squeezed.

Cabinet members, who had been expecting to sign off the final Brexit negotiating position on Tuesday, were told that the issue would hardly be discussed at the meeting beyond an update of the UK’s preparedness for no deal.

Negotiators stayed up until 2.45am on Monday in pursuit of a breakthrough that did not come as the EU made a series of last-minute demands by attaching fresh conditions to the customs backstop, which is designed to come into force if no long-term free trade deal can be signed by the end of 2020.

That failure to progress the talks almost certainly delays agreement at an EU level until a summit scheduled for 13/14 December and makes it increasingly difficult for the critical “meaningful final vote” of MPs on May’s deal to be held before Christmas.

Addressing the lord mayor’s banquet at the Guildhall in London on Monday night, May said: “The negotiations for our departure are now in the endgame”. But in remarks aimed at Brussels negotiators, she added that they could not expect concessions this week just to keep the idea of a November Brexit summit alive.

“We are working extremely hard, through the night, to make progress on the remaining issues in the withdrawal agreement, which are significant,” the prime minister said. “Both sides want to reach an agreement, but what we are negotiating is immensely difficult.”

May’s remarks came as No 10 tried to accuse the EU of trying to bounce the UK into a deal. There had been a brief flurry of speculation at lunchtime, following a report in the Financial Times, that a deal could be close, based on one account of a briefing given by the EU’s chief Brexit negotiator, Michel Barnier, to European ministers. One witness said that Barnier had said “the parameters of a possible agreement are very largely defined”, but No 10 said any suggestion that a deal was close should be taken with “a bucket of salt”.

Labour, meanwhile, is to step up the pressure on the government by launching a bid on Tuesday to force ministers to publish the government’s legal advice on May’s Irish backstop plan before MPs vote to approve her Brexit deal, saying it would be unacceptable for MPs to be kept “in the dark” on how any agreement was reached.

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In Brussels, Barnier told European affairs ministers for the 27 EU members that the negotiators had so far failed to make the decisive progress. “Barnier explained that intense negotiating efforts continue, but an agreement has not been reached yet,” a statement said.

No 10 is faced with a series of emerging demands from the EU, which wants to attach new conditions to the backstop.

Brussels wants the UK to sign up to “dynamic” alignment with state aid and future environmental, social and labour regulations, which would in effect force parliament to cut and paste EU rules into British law.

A commitment on the side of the British to provide the European fishing fleet with access to UK seas after Brexit has also been proposed by member states as a condition for agreement on the customs union.

It is not yet agreed how the backstop can be terminated and there are growing concerns across the Conservative party that it could be used to keep the UK in a long-term customs union with the EU without a say in its regulation. More than 50 hard Brexiters have said they will vote against the Chequers plan, which proposed to keep the UK aligned with EU rules on food and goods after Brexit.

Jo Johnson, the former rail minister who resigned from the government on Friday to support a second referendum , will speak to a rally in Westminster on Tuesday opposing the prime minister’s plan to take Britain out of the EU.

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“I am concerned that a Conservative government is preparing to leave the British people ill-informed over the consequences, with the decision not to publish evidence showing this is a worse deal that the one we already have inside the EU,” Johnson wrote in an article for the Times.

Earlier on Monday, Penny Mordaunt, the international development secretary, became the second cabinet minister in two days to warn that the prime minister did not have a completely free hand in her negotiations with Brussels.

“The important thing is that there’s two checks on this deal – there’s cabinet and there’s parliament. And so cabinet’s job is to put something to parliament that is going to deliver on the referendum result. We need to work together as a cabinet to do that,” Mordaunt said.

Brexiter Andrea Leadsom said on Sunday that she was “sticking in government” to ensure the UK was not trapped in a customs arrangement against its will.

UK sources said last week that they hoped Dominic Raab, the Brexit secretary, could make a visit to Brussels on Tuesday to unveil a deal and prepare the way for a Brexit summit. But No 10 said on Monday that there were no plans for him to make that journey.

EU capitals also want time to examine any agreement made between the European commission and the UK before it is published. France and Germany are understood to have made the point forcefully to Barnier.

The withdrawal agreement, the draft exit treaty, is already running to more than 400 pages of dense legal text. It is expected to be published when a deal is agreed in principle between the UK and the EU, accompanied by a political declaration about the future trade relationship between the two.

Michael Roth, Germany’s minister for the EU, said the member states had made “many compromises but the room for manoeuvre is very much limited and our British friends know exactly where our discussions are”.

Belgium’s deputy prime minister, Didier Reynders, told reporters: “We have time but not so much, so for this moment it’s very difficult to make real progress but before Christmas I’m hoping that it will be possible”.

Simon Coveney, the Irish deputy prime minister and foreign minister, said it was “a very important week for the Brexit negotiations”.

“There is clearly work to do between the two negotiating teams and I think we need to give them time and space now to finish that job,” he said.