Britain has all but given up on a special Brexit summit at the end of November as there remain too many sticking points to complete the talks in the time originally hoped for.

UK and EU negotiators were talking until 2.45am on Monday, Downing Street said, but sources downplayed the prospect of any immediate breakthrough as the impasse on the Irish border backstop continues.

Negotiations will continue intensively this week, but unless there is dramatic progress by the end of Wednesday, there can be no European summit to sign off a draft deal this month. “There’s no breakthrough at the moment,” a Whitehall source said.

The absence of a breakthrough means Tuesday’s scheduled cabinet meeting will not be the substantive discussion intended to sign off the UK’s Brexit negotiating position as had been expected. It will note developments and discuss no-deal planning instead.

A Brexit deal could be signed off at the European Union’s scheduled summit on 13 and 14 December, which would leave little time to squeeze in a parliamentary vote to ratify the agreement before Christmas.

May’s prospects of sealing a Brexit deal markedly reduced as Conservative concern about her negotiating strategy intensified. 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.

“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. And I’m going to be supporting the prime minister to get a good deal for this country,” Mordaunt said.

Earlier, Michel Barnier said a breakthrough had not been achieved in the latest intensive negotiations with the British over the weekend.

During a short meeting in Brussels, Barnier told European affairs ministers for the 27 EU members that the negotiators had so far failed to make the decisive progress needed on the Irish border issue.

“Barnier explained that intense negotiating efforts continue, but an agreement has not been reached yet,” a statement 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. On Friday, rail minister Jo Johnson, a younger brother of Boris, resigned from the government warning the Brexit agreement was becoming “a terrible mistake”.

UK sources had spoken last week of a hope that 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 morning that there were no plans for him to travel to Brussels for the moment.

If an agreement can be secured in the next 36 hours, a November summit could still be convened by Donald Tusk, the president of the European council, leading to the publication of both the withdrawal agreement and the political declaration on the future relationship. May wants to secure a November summit to ensure there is enough time for the British parliament to ratify a deal.

EU capitals, however, 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.

In the meeting with Barnier, about 10-12 member states intervened, stressing the need for national capitals to be able to scrutinise any Brexit deal, including the political declaration on the future. Ministers also welcomed continued no-deal planning and stressed that the EU had to remain united.

To avoid a hard border on the island of Ireland ever emerging, the government is proposing a temporary UK-wide customs union to be in place until another solution is believed possible by Whitehall.

The EU is in turn insisting the UK could not unilaterally withdraw from such an agreement if Whitehall decided that another border solution was possible.

Brussels is also demanding that the UK 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 diktats 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.

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.

“Of course we are prepared for all the different possibilities but we try to work hardly on a good agreement and we are very close, you know what are the limits for the moment.

“About Ireland we have made a proposal with some evolutions in the last days but until now we don’t have a positive signal about that so I’m hoping this will be the case in the next weeks but certainly not today.”

Nathalie Loiseau, the French EU minister, said there had been intensive discussions and Brussels was working to avoid a no-deal scenario, but that the member states would need to go into meticulous detail over the terms of a customs union.

She said: “I have no crystal ball unfortunately. We will have a close look at what a customs union would mean for us because it’s in between the withdrawal agreement and the future relationship so of course it’s a little bit special to discuss the two of it. We are ready, we are open but of course we want to see the details.”

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.