The EU will not agree to the kind of "managed divergence" Britain is believed to favour in its future relationship, sources in Brussels said on Thursday.
Brexit-supporting Conservative MP Michael Fabricant described it as a "total betrayal" of Leave voters.
On Thursday, May took her most senior cabinet ministers away to her Chequers country residence to thrash out an approach to the future trade relationship that they can all agree on. Tea, snacks, drinks, dinner, desserts, talk and drinks were on the agenda.
But the issues still go to the heart of concerns about money and sovereignty and threaten to undermine the EU's efforts to present a united front after the UK leaves next year. After a dinner of cream of sweetcorn soup and slow braised Guinness short rib of beef, her office said: "The way forward will be set out by the PM in a speech next week following discussions at full cabinet".
Prime Minister Theresa May had a positive meeting about Brexit with her ministers, where they agreed upon the basis of her forthcoming speech on the UK's future relationship with the European Union, her spokesman said on Friday.
"The last thing Britain could sensibly do is to leave Europe and then pursue a sort of leftist version of the European social democracy it had just abandoned".
The 27 leaders won't take any formal decisions on Friday but will lay the ground for what could be bitter negotiations ahead, particularly over a post-Brexit funding gap of up to 15 billion euros a year.
Her Brexit blueprint is likely to run into resistance in the European Commission which argues that Britain is attempting to "cherry-pick" elements of the EU single market. "But finding an agreement in the European Council already this year seems really hard", Tusk said. How easy? All unknown.
Davis told the newspaper this week: "There is no final answer".
But former prime minister Tony Blair said the government was not being realistic.
Speaking to the BBC, Health and Social Care Secretary Jeremy Hunt rejected the customs union calls and said it was possible to have "frictionless" trade with the continent without one.
The prime minister is expected to lay out the government's position on Brexit transition in the first week of March.
The odds of stopping Brexit are now close to 50:50, said Eloise Todd, the chief executive officer of "Best for Britain", which is about to launch a major campaign.
Juncker quipped when asked for his thoughts about the meeting that "I am not the British prime minister, it would be good for Britain if I was".
"If you have a family that's had a feud that's run for three generations, it's not going to be sorted out by one Christmas dinner, however good that Christmas dinner might be", said Rob Ford, a professor of politics at the University of Manchester.