A draft of Theresa May’s Brexit plan has already been dismissed as unrealistic by senior EU officials, who say the UK has no chance of changing the European Union’s founding principles.

The prime minister is gathering her squabbling ministers at Chequers on Friday for a one-day discussion to thrash out the UK’s future relationship with the EU. But EU sources who have seen drafts of the long-awaited British white paper said the proposals would never be accepted.

“We read the white paper and we read ‘cake’,” an EU official told the Guardian, a reference to Boris Johnson’s one-liner of being “pro having [cake] and pro-eating it”. Since the British EU referendum, “cake” has entered the Brussels lexicon to describe anything seen as an unrealistic or far-fetched demand.

May’s white paper is expected to propose the UK remaining indefinitely in a single market for goods after Brexit, to avoid the need for checks at the Irish border. While the UK is offering concessions on financial services, it wants restrictions on free movement of people – a long-standing no-go for the EU.

Jean-Claude Piris, a former head of the EU council’s legal service, said it would be impossible for the EU to split the “four freedoms” underpinning the bloc’s internal market, which are written into the 1957 treaty that founded the European project: free movement of goods, services, capital and people.

“The EU is in difficulties at the moment; the one and only success which glues all these countries together is a little bit the money and the internal market,” Piris said. “If you fudge the internal market by allowing a third state to choose what they want ... it is the beginning of the end.”

Some sources expect the UK to abandon these plans. In an attempt to sweeten the pill they are prepared to offer an extra year of transition to smooth Britain’s EU exit.

The British government believes the EU is guilty of its own cherry-picking, for example, by demanding the status quo on fishing quotas in exchange for zero tariffs on goods. Moreover, British officials think a single market in industrial goods is a win for the EU, which sells a surplus of manufactured products to the UK. Piris disagrees: “It is in their short-term economic interest, but it is a short-term myopic view, it is not what the leaders of the EU will do.”

Responding to the latest EU views on the white paper, a UK government source said: “Rather than getting hot under the collar over unfounded media speculation, we’d suggest a better approach would be to wait for the white paper to be published before responding to it.”

Theresa May is hoping for a warmer reception from EU countries. But Spain’s foreign minister has already said an “angry” France and Germany would reject these plans. “Germany will say no, France will say no, Spain will say no,” said Josep Borrell, who also described Brexit as “a pain in the ass”.

At an EU summit on Friday, the EU’s 27 leaders, minus May, spent no more than 15 minutes discussing Brexit, while only three or four countries intervened. A terse statement issued by the leaders called on the UK to come up with “realistic and workable proposals”.

This language was drafted in anticipation that “cake may be coming”, said another EU source, who described expectations of the Chequers meeting as modest.

“The real problem is that if the result of Chequers is not unambiguous, the reality is that a lot of time, the summer, will be lost. And then you are really under a heavy time constraint,” said the source. “Yes, it increases the chances of a no-deal.”

A spokesperson at the Department for Exiting the European Union referred back to remarks made by the Brexit secretary, David Davis, when the government announced the publication of the white paper.

Describing the paper as “our most significant publication on the EU since the referendum”, Davis said: “It will communicate our ambition for the UK’s future relationship with the EU, in the context of our vision for the UK’s future role in the world.” He also said it would “include detailed, ambitious and precise explanations of our positions ... it should set out what will change and what will feel different outside the EU.”