Less than six months before Britain leaves the bloc the Brexit talks were paused on Sunday after the two sides failed to agree on how to deal with the UK's only land border with the EU.

The problem of how to prevent the return of a hard border between the British province of Northern Ireland and EU-member Ireland has become the biggest hurdle to a deal on Brexit.

May, a self-declared unionist who has said repeatedly that she could not countenance the break-up of the United Kingdom, is struggling to find a way to satisfy the demands of not only the EU, but of her Conservative Party and her partners in parliament, Northern Ireland's Democratic Unionist Party (DUP).

For now, there has been little success in narrowing the gap between those competing demands, and Ireland's Foreign Minister Simon Coveney said any deal would now "take a bit more time than many people had hoped".

The DUP, which has threatened to pull support from the government over the backstop row, said it now believed a no-deal Brexit was almost inevitable and described the talks in Brussels as turning into a "battle for the union".

"Given the way in which the EU has behaved and the corner they've put Theresa May into, there's no deal which I can see at present which will command a majority in the House of Commons," said the party's Brexit spokesman Sammy Wilson.

"So it is probably inevitable that we will end up with a no-deal scenario," he said.

May's former foreign minister, Boris Johnson, a bookmakers' favourite to replace May, was equally critical, saying the talks were "now entering the moment of crisis".

"In presuming to change the constitutional arrangements of the United Kingdom, the EU is treating us with naked contempt," he wrote in his weekly column in the Telegraph newspaper.

It was that kind of opposition which made it impossible for May's Brexit minister Dominic Raab to agree to a deal in Brussels on Sunday.

British officials said London could not agree to Brussels' demand to have "a backstop to a backstop", which would see the EU's proposal to keep Northern Ireland in the bloc's customs union if a new trading relationship is not in place in time.

Britain has long said it wants an agreement on a future relationship with the EU, which London sees as including a common rule book for manufactured and agricultural products, which would negate any need for a backstop plan for Ireland.

But EU negotiators have criticised that proposal, and said on Sunday it was clear that, as things stood, May did not feel she could get a deal through her cabinet.

British officials were optimistic of making some progress at the EU summit this week, with foreign minister Jeremy Hunt telling reporters in Luxembourg: "There are one or two very difficult outstanding issues but I think we can get there."

Australian Associated Press