The European Union’s chief Brexit negotiator, Michel Barnier, has told EU ambassadors from the remaining 27 members that unless a deal can be reached before the end of the day on Friday then discussions about Britain’s future relationship with the bloc will have to wait until January.

Mrs May spoke to Irish Taoiseach Leo Varadkar and Democratic Unionist Party (DUP) leader Arlene Foster on Wednesday but does not appear to have made any concrete progress, with Westminster, Dublin and Stormont refusing to back down on their demands.

Diplomats from the EU27 are scheduled to meet on Friday in the hope an agreement will have been reached by then.

However, if there is not a deal on the table, the diplomats have told Mr Barnier they will not have enough time to take the proposed agreement back to be scrutinised ahead of the European Council meeting, which begins on December 14.

Mr Varadkar, appearing alongside his Dutch counterpart Mark Rutte on Wednesday evening, said there was “room to manoeuvre” the deal ahead of the Friday deadline.

Shining hope on a deal being thrashed out in time, he said: “Having consulted with people in London, May wants to come back to us with text tonight and tomorrow. And I expect to move forward as well – I want us to move forward if it’s possible next week.”

However, the progress of the Brexit agreement could still be interrupted by the calendar of European Commission president Jean-Claude Juncker, who is “out of town” on Friday and Saturday and therefore unavailable for talks.

Mrs May is also facing pressure from various groups in Westminster as the Brexit deadlock deepens divisions within the Government.

The Labour party has this week branded the Government’s performance in Brussels an “embarrassment” and a “shambles”, while senior Brexit-backing Tories are unhappy about the idea of the whole of the UK signing up to any “regulatory alignment” with the rest of the EU, as they believe it would defeat the point of Brexit.

Brexiteers, including MP Bernard Jenkin, warned the House of Commons it would be impossible to strike trade deals with other nations if the UK “remains shackled to EU regulation after we’ve left the EU”.

And a group of 19 Remain-backing Tories, including three former cabinet ministers, have told the Prime Minister it is "highly irresponsible" for anyone to dictate terms which may scupper a deal.

In a letter to Downing Street, they accuse ardent Brexiteers of ignoring warnings about the uncertainty a no deal scenario would create.

The group, which includes Nicky Morgan, Stephen Crabb and Dominic Grieve, has urged the Mrs May not to rush into an agreement and concludes by telling her to "take whatever time is necessary to get the next stage of the UK's relationship with the EU right".

On Monday, Northern Ireland's DUP - whose support the prime minister needs to win key votes at Westminster - objected to draft plans drawn up by Britain and the EU.

The party said the proposals, which aimed to avoid a "hard border" by aligning regulations on both sides of the border between Northern Ireland and the Republic of Ireland, were not acceptable. 

Dublin insists it will not agree to any deal that includes a hard border, something Mrs May seems keen to ensure.