She wanted legal assurances on the Irish backstop and had warned the deal itself was "at risk" over the issue.

But European Commission president Jean-Claude Juncker said there could be clarifications but no renegotiation.

Labour says MPs must vote on the deal next week and it was "unacceptable" for it to be pushed back to January.

"This is becoming a farce," said Shadow Brexit Secretary Sir Keir Starmer.

"The prime minister pulled this important vote last week on the basis that she was going to get meaningful changes to her Brexit deal, She has obviously not."

On Thursday evening, Mr Juncker urged the UK to set out more clearly what it wants, adding that the European Commission will publish information on 19 December on its preparations, should the UK leave the EU without a deal in place.

"Our UK friends need to say what they want, instead of asking us to say what we want, and so we would like within a few weeks our UK friends to set out their expectations for us, because this debate is sometimes nebulous and imprecise and I would like clarifications," he said.

Pooled video footage from the summit on Friday showed Mrs May and Mr Juncker engaged in what appeared to be a tense exchange, following his comments.

The Democratic Unionist Party, on whom Theresa May relies for her Commons majority, said the EU's response was unsurprising and Mrs May must not "roll over as has happened previously".

"The EU are doing what they always do," said the party's leader Arlene Foster. "The key question is whether the prime minister will stand up to them."

But Cabinet minister David Lidington described the meeting as a "welcome first step" in showing that the EU was committed "to negotiate a trade deal with the UK speedily".

Mrs May travelled to Brussels to make a special plea to EU leaders after delaying Tuesday's Commons vote on the deal, in anticipation of a heavy defeat.

She then went on to win a confidence vote brought by her own MPs but vowed to listen to the concerns of the 37% of Tory MPs who voted against her and was hoping to address their concerns about the controversial "backstop" plan in the withdrawal agreement.

Critics say the backstop - aimed at preventing a hard border in Northern Ireland - would keep the UK tied to EU rules indefinitely and curb its ability to strike trade deals.

Conservative MPs have demanded changes to make it clear that it could not last forever, and the UK could terminate the arrangement on its own.

If this meeting was meant to provide Theresa May with the beginnings of an escape route from her Brexit conundrum, the signs are nothing less than awful.

At one of her most vulnerable political moments, Number 10 was hopeful at least of an indication of a potential solution to the most intense of a long list of Brexit problems - the controversial so-called backstop, designed to guarantee there would be no hard Irish border.

But right now, that's simply not on offer.

EU leaders made it plain that their warnings - that their divorce deal with Britain was not up for negotiation - were real.

In comments released by Downing Street on Thursday, Mrs May urged EU leaders to help her "get this deal over the line" and said she firmly believed it could get through the Commons, saying: "There is a majority in my Parliament who want to leave with a deal so with the right assurances this deal can be passed. Indeed, it is the only deal capable of getting through my Parliament," she said.

Mrs May urged EU leaders to work with her to "change the perception" of the controversial backstop plan.

But European Council president Donald Tusk said the withdrawal agreement was "not open for renegotiation" although he stressed the backstop was "an insurance policy", saying it was the EU's "firm determination" to work "speedily" on alternative arrangements.

BBC Brussels reporter Adam Fleming said the fact that the EU said it would use its "best endeavours" to get a future trade deal that would get rid of the need for a backstop - even if the backstop came into force - was seen as important by British officials who said it meant the UK could go to an independent arbitration panel if they felt the EU was dragging its feet.

But he said Ireland had requested that the European Council conclusions be toughened up and a paragraph which suggested further work would be done to reassure the UK was removed because "there was no support" for it.

'Crisis mode'

Downing Street has confirmed MPs will not now vote on Mrs May's deal before Christmas, and said the vote would happen "as soon as possible in January".

Conservative Brexiteer Mark Francois told the BBC: "It is as plain as a pikestaff that this will never get through the House of Commons... the prime minister, I'm afraid, is completely boxed in."

The Labour former PM Tony Blair told the BBC he believed a majority of MPs in the Commons would back another referendum on Brexit, if Parliament could not agree on another way forward:

"I think that will happen if it is clear that there is no majority for any one form of Brexit," he told Radio 4's Today.

"We have had 30 months of negotiation and let's be clear - we are in crisis mode on this."