The European Union insisted that a “fully workable and legally operational” solution to the Irish border issue must be included in any Brexit deal, after suggestions from the UK that the details could be worked out after October 31.

Brussels’ chief negotiator Michel Barnier and Steve Barclay met for talks described as “serious, detailed discussions” by the Brexit Secretary.

The UK has put forward a “first set of concepts, principles and ideas”, Brussels said, but it was “essential” that a way of avoiding a hard border with Ireland was included in the Withdrawal Agreement.

Prime Minister Boris Johnson has insisted that the backstop – the contingency plan which will keep the UK closely tied to EU rules if no other measures are in place to avoid a hard border – must be scrapped.

Mr Barclay has suggested that the final details of alternative arrangements would not necessarily have to be agreed until December 2020, if a deal can be reached.

But in a statement following the talks between Mr Barclay and Mr Barnier, the European Commission said: “It is essential that there is a fully workable and legally operational solution included in the Withdrawal Agreement.

“We remain willing and open to examine any such proposals that meet all the objectives of the backstop.”

Mr Barnier said the work on Brexit would continue with “full respect” to the UK, “our partner and ally”.

But he added: “The EU will remain vigilant and continue to apply all EU principles and values.”

Their meeting came after Ireland  played down the prospect of an imminent Brexit breakthrough, pointing to a “wide gap” between Mr Johnson’s position and that of the European Union.

Simon Coveney, Ireland’s deputy prime minister, said: “There are serious problems that arise because of the change in approach by the British Prime Minister – asking to remove a very significant section within the Withdrawal Agreement without any serious proposals as to how you solve those problems is not going to be the basis for an agreement.

“That’s why I think there is an onus on the British Government to come forward with alternative arrangements – if they have them – which can resolve the Irish border question.”

He told BBC Radio 4’s Today programme that Ireland is being asked to replace a “guarantee around that border question” with a promise that “somehow we’ll do our best”.

He said: “We want to find a solution, we want to get a deal, and we want to allow the UK to leave the EU in an orderly and sensible manner, but we cannot allow Ireland to be the collateral damage of that.

“I think for Britain to ask us to do that is a very unreasonable request, and it won’t be the basis of a deal.”

Mr Johnson wants to scrap the backstop because of concerns it could leave the UK indefinitely tied closely to Brussels’ rules.

Dutch Prime Minister Mark Rutte suggested a deal would be possible by October 31 – “with a few nights of hard work a lot can be done” – but the UK must produce “real, specific proposals”.

Further Brexit talks will take place in the US next week as world leaders gather for the United Nations general assembly.

European Council president Donald Tusk will meet Irish leader Leo Varadkar and Germany’s Angela Merkel before sitting down with Mr Johnson on Monday in New York.