Theresa May has said she believes a deal on the UK’s orderly withdrawal from the EU remains “achievable”, despite the deadlock in negotiations ahead of a crunch Brussels summit.

The Prime Minister was due to address leaders of the 27 remaining EU states before they discuss Brexit in her absence at the European Council on Wednesday evening.

But leaders were openly saying that there would be “no breakthrough” at the summit, which was long billed as the “moment of truth” when a deal must be done to give time for ratification by the date of Brexit on March 29 2019.

Arriving in Brussels, Mrs May insisted there had been “very good progress” since last month’s meeting in Salzburg, when she was humiliatingly told that her Chequers plan for Brexit would not work.

But she acknowledged that differences remain over the key issue of the “backstop” arrangement to keep the Irish border open in the absence of a broader trade deal.

Theresa May arrives in Brussels to brief the remaining 27 EU leaders (European Commission Audiovisual Services)

“We have solved most of the issues in the withdrawal agreement,” said Mrs May.

“There is still the question of the Northern Irish backstop.

“But I believe everybody around the table wants to get a deal. By working intensively and closely, we can achieve that deal.

“I believe a deal is achievable and now is the time to make it happen.”

Before travelling to Brussels, Mrs May vowed to protect the “precious Union of the United Kingdom” as she answered questions in the House of Commons.

However, during exchanges at Prime Minister’s Questions, Labour leader Jeremy Corbyn said the Tories were too “weak and divided” to negotiate effectively with Brussels.

Mrs May told MPs: “We will not accept any proposals which would effectively break up the United Kingdom.”

Earlier, Ireland’s deputy prime minister Simon Coveney confirmed the EU’s chief negotiator Michel Barnier was prepared to extend the 21-month transition period after Britain leaves the bloc to allow time to negotiate an alternative arrangement.

“What Michel Barnier has indicated very clearly is that the EU side, certainly, is willing to allow more time in the transition period to agree an alternative solution to a backstop,” Mr Coveney told BBC Radio 4’s Today programme.

However, there was little enthusiasm for the idea in London, with Government sources insisting Downing Street was not looking for an extension to transition arrangements.

And Mrs May did not respond when asked whether she would welcome an additional year’s transition.

The meeting in Brussels was supposed to be the occasion when the leaders of the EU 27 member states gave the green light for a special summit in November to finalise the terms of Britain’s withdrawal.

However, European Council president Donald Tusk has warned that without new “concrete proposals” from the British to break the logjam over the Irish border backstop, further progress on a deal may be impossible.

In a speech to the German parliament before travelling to Brussels, Chancellor Angela Merkel said that the possibility of a Brexit deal was “still there”, but added that Berlin was making plans for a no-deal withdrawal.

And in Paris, Emmanuel Macron’s government published details of legislation to authorise preparations for a no-deal Brexit, which could see the restoration of customs checks and health inspections for animals at French ports, and even a requirement for Britons to seek visas for stays of three months or more.

Ahead of this evening’s meeting, Mrs May was having bilateral meetings with Mr Macron as well as European Commission president Jean-Claude Juncker, Mr Tusk and Irish Taoiseach Leo Varadkar.

Mrs May was greeted in Brussels with a kiss from European Commission president Jean-Claude Juncker (European Commisison Audiovisual Services)

Ahead of her visit to Brussels, Mrs May was able to secure the backing of her Cabinet, at least for now, amid reports that some Brexiteer ministers had been prepared to quit if she gave too much ground to Brussels.

However, there was anger among Tory Brexiteers after The Daily Telegraph reported that Chancellor Philip Hammond warned the UK could still have to pay the EU up to £36 billion of the £39 billion “divorce bill” to settle its outstanding liabilities, in the event of a no-deal break.