Theresa May has insisted she is convinced she will get a deal on Britain’s withdrawal from the EU, despite a “moment of truth” summit passing with no sign of a breakthrough.

The Prime Minister infuriated MPs from all sides of her party by indicating she is ready to delay the UK’s final departure from EU structures until 2021 in the hope of breaking the deadlock over the Irish border.

Just a month after the humiliating Salzburg summit at which her Brexit proposals were roundly dismissed by EU leaders, Mrs May said there was now a “very real that people want that deal done”.

But she admitted that there were “more difficult moments” to come before agreement is reached.

And Emmanuel Macron left no doubt that he believes the ball is now firmly in Britain’s court to deliver a compromise to ensure that the border between Northern Ireland and the Republic can stay open.

“This is a question of British political capacity to find a presentable deal,” said the French president.

And he broke into English as he said: “Now the key element for a final deal is on the British side, because the key element is a British political compromise…

“There is no additional compromise to be made on the European side.”

The two-day European Council summit has long been pencilled in as a “moment of truth” when agreement must be reached to provide time for ratification and avoid the UK crashing out without a deal on March 29 2019.

But no deal was found, and the leaders of the 27 remaining EU states decided not to call a special Brexit summit in November after chief negotiator Michel Barnier said he needed “much more time” for talks.

There was no mention of Brexit in the five pages of conclusions released at the end of the two-day gathering.

In a press conference at the end of the summit, Mrs May said good progress was being made on the UK’s withdrawal agreement, but acknowledged that “a few, but considerable, outstanding issues” remained to be resolved.

“There is a lot of hard work ahead, there will be more difficult moments as we enter the final stages of the talks, but I’m convinced we will secure a good deal that is in the interests of the UK and of the European Union,” she said.

Belgium EU BrexitTheresa May addressed fellow EU leaders on Brexit (Alastair Grant/AP)

Mrs May declined to put any fixed date on the possible extension to the UK’s transition period, which she has said could last “a matter of months” into 2021.

UK officials stressed that the move was not being proposed by the UK but the PM was ready to consider it.

It is thought that the extra time may give negotiators leeway to resolve the question of how to construct a “backstop” which would keep the Irish border open in the absence of a broader trade deal.

Brexiteers reacted with fury to the idea of the transition – during which the UK would remain in the single market and customs union and subject to EU rules – being extended beyond the end of December 2020, at  a potential cost of billions of pounds in contributions to EU budgets.

The chairman of the influential European Research Group of Eurosceptic Tory MPs, Jacob Rees-Mogg, said it would mean “we are in the EU for longer when the EU can make rules for the UK over which we would have no say and we would be paying for the privilege”.

And former minister Nick Boles – who is backing the “soft Brexit” option of temporary Efta membership – warned that Mrs May was “losing the confidence now of colleagues of all shades of opinion”.

Scotland’s constitutional relations secretary Michael Russell said the summit had been “yet another humiliation for the Prime Minister”, warning: “Tory divisions are paralysing the UK Government and leading Scotland to the brink of a catastrophic no deal outcome.”

Countdown to Brexit: key events. (PA Graphics)

And DUP deputy leader Nigel Dodds said the extension would mean the UK “continues to ‘pay but have no say’ in Brussels”, while failing to resolve the objections to the EU’s backstop of his party, which props up Mrs May’s minority administration in the Commons.

Former Ukip leader Nigel Farage said the proposed delay would bring the UK’s final departure so close to the 2022 general election that it “may mean we never leave at all”.

Leave-backing Cabinet ministers Michael Gove and Penny Mordaunt also signalled concern that Britain’s withdrawal from the EU should proceed swiftly.

But Mrs May insisted that any delay would “only be for a matter of months”, adding: “This is not expected to be used, because we are working to ensure that we have that future relationship in place by the end of December 2020.”

UK officials said that Mrs May continues to regard the EU backstop – under which Northern Ireland would remain within the European customs union until a broader trade agreement was finalised – as “unacceptable”.

German Chancellor Angela Merkel – who joined Mr Macron and the prime ministers of Belgium and Luxembourg for a late-night beer in a Brussels cafe on Wednesday – insisted that all of the EU27 want a deal guaranteeing a good relationship with the UK.

And, in comments cited approvingly by Mrs May, she added: “I think where there is a will there is a way. That is usually the way.”

Meanwhile, Spanish Prime Minister Pedro Sanchez said the future status of Gibraltar “is resolved” and “won’t be a problem” for Britain’s plans to leave the EU.

European Council president Donald Tusk said he stood ready to convene a new Brexit summit “if and when” decisive progress has been made.

“We are in a much better mood than after Salzburg,” he said. “What I feel today is that we are closer to final solutions and the deal.”

But he added: “We should be clear that for now, not enough progress has been made.”

Mr Tusk said the EU27 would be ready to “consider positively” any proposal from the UK for an extended transition period, something which Mr Juncker said “probably will happen”.