The chances of Theresa May striking a deal with Brussels on the Irish border that she can sell to the cabinet and parliament are said by EU officials to be “50-50” as the fraught talks enter their final stretch.

The British negotiating team and the European commission’s taskforce, led by Michel Barnier, are to enter a secretive phase known as the “tunnel” this week, but senior EU figures involved in the talks warned the competing redlines remain “incompatible” in key areas.

The British government has set out its stall to make “decisive progress” on the issue of the Northern Ireland backstop by Friday, in the hope that Donald Tusk, the president of the European council, could then call an extraordinary Brexit summit for the end of the month to seal the deal.

One Whitehall source said, should sufficient ground be made in the coming days, a tentative new date of 22 November is being floated for a meeting of the EU’s heads of state and government.

Downing Street has insisted it does not have a deal ready for signoff, in response to reports over the weekend of there being an agreement in the making.

“We are not sitting on powder keg knowledge that we have signed a secret deal,” the No 10 source said. “We are not on the cusp of some seismic shift.”

Some at the highest levels of government fear that, unless progress is agreed by Tuesday when the May sees her senior ministers and parliament breaks for recess, the cabinet may not have a direct input before a summit announcement is made.

“The reality is that we need a November summit more than the EU do,” a government source said. They suggested that a December deal would mean not only a later parliamentary vote but would require spending on no-deal planning and changes to the roles of hundreds of civil service.

There is chance of progress being made in order for an emergency summit to be called on Friday, government insiders believe, suggesting it is possible the cabinet will not be directly involved if it was last-minute. “It is high stakes,” the source said.

EU officials and diplomats cautioned against the optimism expressed by some about the imminence of a breakthrough, describing the chances of striking a deal that meets both sides needs as “50-50”.

Brussels has so far insisted the withdrawal agreement must contain legal text that could keep Northern Ireland in effect in the customs union and single market as Britain leaves.

The commission has accepted that an all-UK customs union could be referenced and prioritised in the agreement, with a separate treaty, negotiated during the transition period, filling out the details.

An EU official suggested that such a UK-wide customs deal could only replace the Northern Ireland-specific text if it was a permanent arrangement, and even then there would serious legal issues with making such a commitment at this stage.

“There is an evolution in the commission’s thinking. From what they originally proposed, there is a shift towards the UK in terms of the UK-wide thing so, yes, flexible, but whether that flexibility will lead to agreement is something else,” the official said.

The source said any hope of Northern Ireland-specific customs arrangements being removed would involve a “huge jump on the UK side”.

The official suggested that May would need to make a “calculation about what is sellable and how she sells it but it does not correspond to the buccaneering Britain of Bojo [Boris Johnson]”.

Even with an all-UK customs deal at the heart of the withdrawal agreement, there would need to be Northern Ireland-specific elements in terms of both single market regulatory checks and customs.

Exporters entering the Republic from Northern Ireland would, in the normal run of things, need to prove that their goods are from a country that is in a customs union with the bloc and that they have a rule of origin waiver.

Fabian Zuleeg, chief executive of the leading EU thinktank the European Policy Centre, said he did not believe it would be possible for the EU to satisfy the prime minister’s demands, and that the lack of realism in the UK increased the chances of a no-deal Brexit.

He said: “I don’t see the EU willing to accept a deal without the Northern Ireland-specific backstop.

“What I have found concerning is that people are making very categorical statements that no British prime minister can sign a backstop on Northern Ireland which seems to go against what is agreed in December, and you hear it not from the government but also the opposition. That makes me think we are moving very quickly to a no deal.”

EU diplomats have also scorned the prime minister’s suggestion that significant progress has been made on the political declaration on the future trade deal, with the economic aspects described as a “raw nerve” where the two sides are “talking about different things”.

The prime minister is seeking a commitment to arrangements, including a common rule book that could deliver “frictionless trade”.

Barnier has repeatedly said that this is not possible, and diplomats believe a weaker pledge for trade flows to be “as frictionless as possible” is the most likely outcome.

Number 10 has said it would not accept a deal that would be as wide-ranging as some reports have suggested, encompassing May’s Chequers plan for a “common rule book”, as well as leaving the door open for a possible Canada-style deal.

“We have said that we will come up with a ‘precise’ future partnership,” the Whitehall source said. “That will not be all things to all men. It will be a detailed political agreement which we can use to forge our future trading relationship.”