THERESA May has appealed to Brussels not to “derail” the Brexit talks over the Irish border issue as she insisted that a deal with the EU was still “achievable” even though negotiations might run on into December.

In a Commons statement, the Prime Minister called for "cool, calm heads to prevail," stressing how she did not believe the UK and the EU were far apart but expressed frustration that virtually all the remaining points of disagreement centred on the so-called “backstop”.

She told MPs: “We cannot let this disagreement derail the prospects of a good deal and leave us with the no-deal outcome that no-one wants. I continue to believe that a negotiated deal is the best outcome for the UK and for the European Union. I continue to believe that such a deal is achievable.”

Mrs May was addressing the House of Commons just two days before she travels to Brussels for a summit at which it had initially been hoped to finalise the UK's withdrawal agreement as well as a political declaration on future trade and security relations.

Following the failure to achieve a breakthrough when Dominic Raab, the Brexit Secretary, met Michel Barnier, the EU chief negotiator, on Sunday, the European Commission confirmed that no further negotiations would be held ahead of Thursday's summit.

It was still unclear when the PM would make her Brexit presentation to her fellow leaders as it is expected that she will not attend the pre-summit EU27 dinner on Wednesday evening.

Last night, the PM was due to talk to Emmanuel Macron, the French President, and is likely to talk to more EU counterparts before she heads off to the Belgian capital tomorrow.

Donald Tusk, the European Council President, tweeted: “It always seems impossible until it's done. Let us not give up.”

Angela Merkel, the German Chancellor, said the prospect of an agreement "looks a bit more difficult again", adding: "If it doesn't work out this week, we must continue negotiating, that is clear. But time is pressing."

Talks at the weekend foundered over the EU's demand for a "backstop to the backstop" designed to ensure that the border between Northern Ireland and the Irish Republic remains open under any circumstances.

Mrs May has offered to keep the whole of the UK temporarily in a customs union with the EU until a broader trade deal is in place avoiding the need for customs and regulatory checks at the Irish border with the expectation that this would be no later than the end of 2021.

Yet, Mr Barnier insisted that a carve-out keeping Northern Ireland alone in the EU's customs area should remain available in case the UK-wide arrangement lapsed before the trade deal was finalised.

However, the PM told MPs that this was not acceptable as it risked undermining the integrity of the UK.

“They want this to be the Northern Ireland-only solution that they had previously proposed. We have been clear we cannot agree to anything that threatens the integrity of our United Kingdom,” she declared to Conservative cheers.

Jeremy Corbyn said MPs had been presented with another “Groundhog Day” moment, dismissing Mrs May's comments as "another 'nothing has changed' moment from this shambles of a Government".

The Labour leader insisted the UK and EU should negotiate a "permanent customs union" to protect jobs and manufacturing.

But Boris Johnson, the former Foreign Secretary, hit back, saying by backing a customs union Mr Corbyn was guilty of a “shameless U-turn and a betrayal of millions of people who voted Leave".

Peter Grant for the SNP urged Mrs May to commit to a “damage-limitation Brexit” and accept there was a significant consensus for remaining in the single market and the customs union.

“I say to her to ignore her own career prospects, to ignore the career ambitions of those behind her and to look instead at the hundreds of thousands of people whose jobs are at risk if this goes wrong,” added the MP for Glenrothes.