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However Mr Juncker and Mrs May said another round of formal talks will take place at the end of this week in a bid to resolve remaining sticking points.

Mr Juncker said he was 鈥渟till confident we can reach sufficient progress before the European Council of December 15.鈥�

He said the parties 鈥渘ow have a common understanding on most relevant issues, with just two or three open for discussion,鈥� and the EU is ready to resume discussions with the UK.

The sides 鈥渘arrowed our positions to a huge extent today鈥�, he said, adding: 鈥淭his is not a failure and I鈥檓 confident we will reach agreement in this very last round.鈥�

Mrs May said both sides had worked hard in good faith and a lot of progress had been made.

鈥淚t鈥檚 clear, crucially, that we want to move on together鈥�. And I am also confident that we will conclude this positively.鈥�

The race is on to come to what the EU calls 鈥榮ufficient progress鈥� on all the key elements of the exit deal, that is to say expat rights, the Northern Ireland border and the exit bill.

Northern Ireland has been the most controversial issue in these last days, and the UK is rumoured to have offered to accept 鈥榬egulatory alignment鈥� of Northern Ireland with Ireland as a strategy to make a 鈥榟ard border鈥� unnecessary.

This is said to equate to much the same as Northern Ireland staying in the EU's single market and customs union, which the UK had said it wants to leave.

The rumours have already sparked controversy, with the DUP party, on whose support Mrs May鈥檚 Conservatives rely for a majority in parliament, saying it does not want a different regime in Northern Ireland from the rest of the UK.

Meanwhile the first minister of Scotland and the mayor of London have asked if they may have similar special opt-outs for their areas.