Theresa May’s hopes of rescuing a deal to kickstart the faltering Brexit talks have hit fresh trouble after crunch talks with the Democratic Unionist Party (DUP) were delayed.

The Prime Minister had expected to speak to Arlene Foster, the DUP leader, by telephone to convince the party it has nothing to fear over trading rules to avoid a hard Irish border.

But, after twice telling journalists the call was set to take place today, No 10 was forced to admit later that it did not know when the crucial conversation would go ahead.

“The call will happen whenever it happens,” a Downing Street source said.

It appeared the DUP believed that little would be achieved from a direct conversation between the two leaders until major changes were made to a proposed deal on the border.

Earlier, the DUP criticised the “ambiguity” behind a plan for “regulatory alignment” with the EU to avoid a hard border – explaining why, 24 hours earlier, the party had forced Ms May to pull the plug on a deal.

Ms Foster’s apparent snub of the Prime Minister – even as she carried out media interviews – was illustrated by Ms May holding talks with Michelle O’Neill, the Sinn Fein leader in Belfast.

The pair had been expected to discuss a pledge by David Davis, the Brexit Secretary, that appeared to point the way to a potential breakthrough.

Mr Davis surprised MPs by insisting any regulatory alignment with the EU would apply across the UK, rather than see Northern Ireland treated differently.

He revealed the policy during an emergency Commons statement during which Keir Starmer, Labour’s Brexit spokesman, branded the Government’s Brexit strategy an “embarrassment” – and condemned the “coalition of chaos”.

Asked about keeping regulations in step with Brussels, Mr Davis said: “The presumption of the discussion was that everything we talked about applied to the whole United Kingdom.”

However, the plan is likely to be opposed by Brexit-backing Tory MPs, who view the freedom to pursue new trade deals outside the EU – with different regulations – as essential.

Jacob Rees-Mogg fired a warning shot in the Commons, telling Mr Davis that the benefits from “regulatory divergence” had to be “indelible red lines”.

A second Brexiteer, former Northern Ireland Secretary Owen Paterson, urged Ms May to walk away from the negotiating table if necessary, saying: “She should come back with no deal.”

And Iain Duncan Smith said the EU had to be told to “back off – otherwise we will get on with other arrangements that will not be beneficial to you”.

The Prime Minister’s spokesman refused repeatedly to say whether Mr Davis had been “speaking for the Government” – or had Cabinet backing – when he proposed UK-wide regulatory alignment.

In recent weeks, there have been growing tensions between Ms May and her Brexit Secretary, with claims he has been frozen out of the negotiations.

Meanwhile, the EU Commission president appeared to tighten the new deadline for London to present acceptable proposals to ensure no hard land border and allow the talks to progress to future trade.

Jean-Claude Juncker said he would meet Ms May “maybe tomorrow, maybe the day after tomorrow” but “not on Friday and Saturday because I’m out of town”. He added: ”I’m very confident that we’ll do it.”

Earlier, Ms Foster insisted her party would not bend to Dublin’s wishes, saying: “The Irish Prime Minister can be as unequivocal as he likes. We’re equally unequivocal.”

However, her Westminster leader, Nigel Dodds, said the party would accept cooperation with Dublin provided it did not mean following “the rules of the single market or the customs union”.

The DUP did not receive the Prime Minister’s proposals to avoid a new hard Irish land border until Monday morning – as they were about to be presented in Brussels, he said.

The plans had “far too much ambiguity and didn’t actually nail down the issue that needed to be nailed down,” he told a Commons press conference.

The explanation added to criticism of Ms May for failing to win the backing of the DUP – her partners in Government – ahead of resuming the negotiations in Brussels.

The proposed deal unravelled after the DUP attacked any move “which separates Northern Ireland economically or politically from the rest of the United Kingdom”.

It was clear the DUP believed regulatory alignment on both sides of the Irish border, to avoid customs checks and posts, would only apply in Northern Ireland.

In his statement, Mr Davis said there was no question of Northern Ireland remaining in the EU single market or customs union, because the Government would not “leave one part of the United Kingdom behind”.

He insisted regulatory alignment would not mean “harmonisation” on trade, or having “exactly the same rules”. The UK would still be “choosing our own laws”.

Pro-EU MPs seized on the confusion to press for the case for the Government to accept the only solution was for the entire UK to remain within the EU’s economic structures.