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 admitted that there were "more difficult moments" to come before agreement is reached.

But she said she had found "a very real sense that people want that deal done" among her fellow leaders, citing positive comments from German Chancellor Angela Merkel - who she was meeting later in the day for face-to-face talks - and European Commission president Jean-Claude Juncker.

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

But no deal was reached, 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.

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.

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.

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.

The chairman of the influential European Research Group of Eurosceptic Tory MPs, Jacob Rees-Mogg, accused the Prime Minister of "a rather poor attempt at kicking the can down the road".

An extended transition period "means 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", the North East Somerset MP told Sky News.

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", and repeated the Scottish Government's call for the UK to remain in the European single market and customs union.

"Tory divisions are paralysing the UK Government and leading Scotland to the brink of a catastrophic no deal outcome," he said.

Mr Russell added: "Any extended transition period must be for a clear purpose, and the EU has repeatedly said this cannot be a substitute for agreement on the Northern Ireland backstop."

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".

There was no confirmation from UK sources of reports that Brussels and Dublin might now be prepared to consider accepting London's proposal of a UK-wide backstop to be negotiated alongside the framework for future relations.