- Video report by ITV News political correspondent Paul Brand
The European Union's chief Brexit negotiator has suggested a deal with Britain might not be struck before November, after talks hit an impasse over the weekend.
Speaking on the eve of an EU leaders' summit in Brussels, Michel Barnier said several issues needed to be dealt with, including the future of the Irish border.
"We are not there yet," he told reporters, adding: "We need more time".
Theresa May held a more than three-hour Cabinet meeting, in which she told her Government colleagues: "I'm convinced that if we as a Government stand together and stand firm, we can achieve this."
The EU is demanding new "concrete proposals" from Mrs May on how to end the deadlock in Brexit talks, warning that a breakthrough may not be possible without further movement from the UK.
Mrs May will address the remaining 27 EU leaders before Wednesday's Brussels meeting, which had been billed as "the moment of truth" for Brexit but now seems certain to pass without a deal on the UK's withdrawal.
Speaking after being briefed by the EU's chief negotiator Michel Barnier, Mr Tusk said he saw "no grounds for optimism" ahead of the European Council summit.
"As I see it, the only source of hope for a deal for now is the goodwill and determination on both sides," Mr Tusk told a Brussels press conference. "However, for a breakthrough to take place, besides goodwill we need new facts.
"Tomorrow I am going to ask Prime Minister May whether she has concrete proposals on how to break the impasse. Only such proposals can determine if a breakthrough is possible."
There was speculation about the future of some ministers after a group met over pizza on Monday evening to discuss the negotiations.
But the Cabinet remained intact after the lengthy meeting, with the PM's spokesman saying there was strong support from ministers for Mrs May's insistence that any Brexit deal must maintain the integrity of the Union and cannot keep the UK indefinitely in a backstop customs arrangement.
No minister indicated that they might be considering resigning over Brexit during the meeting.
Mr Barnier's comments appear to have more or less put paid to any prospect of a decisive breakthrough at this week's summit.
Since the Brexit discussions began over 18 months ago, the summit had been earmarked as the most likely date for any agreement given the need to get necessary parliamentary approvals before Britain officially leaves the EU next March.
But talks last weekend failed to bridge differences between the UK and EU over the future status of the border in Ireland.
On the eve of the summit, Germany's Europe minister Michael Roth said his message to Mrs May was: "Take responsibility and be constructive."
In a letter to EU leaders ahead of the summit, the president of the European Council Donald Tusk said: “As things stand today, it has proven to be more complicated than some may have expected.
“We should nevertheless remain hopeful and determined, as there is good will to continue these talks on both sides.
“But at the same time, responsible as we are, we must prepare the EU for a no-deal scenario, which is more likely than ever before."