The whole of the UK could align its regulations in certain areas with the EU following Brexit, David Davis has suggested.

Mr Davis was speaking as Prime Minister Theresa May engaged in an intensive effort to restore momentum to Brexit talks which broke up in disarray on Monday.

Irish premier Leo Varadkar said that “the ball is now in London’s court”, after Mrs May pulled out of a proposed deal when the Democratic Unionist Party (DUP) made clear it would not accept proposals for “regulatory alignment” with the Republic.

In a scathing assessment of the turmoil surrounding the talks, Labour’s Sir Keir Starmer said that the “DUP tail is wagging the Conservative dog”.

He urged Mrs May to “rethink her reckless red lines” and put the option back on the table of the UK remaining within the European single market and customs union.

Mrs May was expected to speak to DUP leader Arlene Foster and Sinn Fein’s Michelle O’Neill on Tuesday, and is due to visit Brussels again later this week to try to finalise a divorce deal which would allow leaders of the 27 remaining EU states to give the green light to trade talks next week.

But Downing Street suggested that negotiations could go right up to the wire at the leaders’ summit in the Belgian capital on December 14.

In a statement to the House of Commons, Mr Davis said the UK was now “close” to concluding the first phase of Brexit negotiations, dealing with the Irish border, citizens’ rights and the UK’s financial settlement.

He insisted the Government would not accept any deal which saw Northern Ireland treated differently from the rest of the UK as the price of keeping an open border with the Republic.

But he side-stepped a demand from prominent Brexiteer Jacob Rees-Mogg to make it an “indelible red line” that the UK should be able to diverge from EU rules and regulations after withdrawal, telling him only: “The red line for me is delivering the best Brexit for Britain.”

Mr Davis stressed that “alignment” did not mean full harmonisation with EU regulations, telling MPs: “It’s sometimes having mutually recognised rules, mutually recognised inspection, all of that sort of thing as well – and that’s what we are aiming at.”

(PA Graphics)(PA Graphics)

He added: “There are areas where we want the same outcome but by different regulatory methods.

“We want to maintain safety, we want to maintain food standards, we want to maintain animal welfare, we want to maintain employment rights. We don’t have to do that by exactly the same mechanism as everybody else. That’s what regulatory alignment means.”

But Sir Keir told the Commons: “The question for the Government today is this: Will the Prime Minister now rethink her reckless red lines and put options such as a customs union and single market back on the table for negotiation?

“Because if the price of the Prime Minister’s approach is the break-up of the union and reopening of bitter divides in Northern Ireland then the price is too high.”

DUP deputy leader Nigel Dodds revealed that the party was not shown the draft text of the proposed agreement on the Irish border until the “late morning” on Monday, shortly before Theresa May was expected to sign off on it in a lunchtime meeting with European Commission president Jean-Claude Juncker.

Nigel Dodds and fellow Westminster DUP MPs outside ParliamentNigel Dodds and fellow Westminster DUP MPs outside Parliament (Jonathan Brady/PA)

But in a pointed rebuff to the DUP, Mr Varadkar said that he would listen to “all political parties in Northern Ireland and recognise that the majority did not vote to leave the European Union”.

The Taoiseach said he accepted Mrs May and her team were negotiating “in good faith”, telling the Dail he was “looking forward to hearing from them as to how they think we can proceed”.

But in a clear sign he believes it is for Britain to make further concessions, he added: “The ball is now in London’s court.”

Meanwhile, Mrs May came under pressure from Scottish Conservative leader Ruth Davidson, who said in a tweet that no Tory Government should “countenance any deal that compromises the political, economic or constitutional integrity of the United Kingdom”.

Scottish First Minister Nicola Sturgeon called on Labour leader Jeremy Corbyn to “get his act together” and unite with Remain-backing Tories to “force a different, less damaging Brexit leaving the UK in the single market and customs union”.

And the Government’s approach received a withering assessment from ex-Labour leader Ed Miliband.

He tweeted: “What an absolutely ludicrous, incompetent, absurd, make it up as you go along, couldn’t run a piss-up in a brewery bunch of jokers there are running the government at the most critical time in a generation for the country.”

DUP leader Arlene Foster said her party had been asking the Government for sight of draft texts of the proposed agreement with the EU for five weeks, before a version was finally sent late on Monday morning.

“We hadn’t seen any text, despite asking for text for nearly five weeks now, we haven’t been in receipt of any text and the text only came through to us late yesterday morning,” she told RTE.

“And obviously once we saw the text we knew it wasn’t going to be acceptable.”