The Brexit secretary said it was "not something the Government was considering", as he sent a message to Scotland's Nicola Sturgeon and London Mayor Sadiq Khan who were "banging  the tattered drum of independence". 

He accused them of "making a foolish mistake" as he said "no UK government let alone a Conservatoive Unionist one" would accept the UK remaining in the customs union after Brexit. 

Anna Soubry MP waded into the debate saying "regulatory alignment could be a solution"  and "if it is good enough for Northern Ireland it is good enough for the rest of the country".

But Mr Davis replied: "You can take it as a guarantee from me, we will not be treating any part of the United Kingdom any differently from any other part. 

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"We were elected on a manifesto to leave the customs union and the single market." 

The Tory politician insisted the PM was "now close to concluding the first phase and moving on to talking about trade" with the EU, telling the chamber: "All parties remain confident of a positive conclusion by the end of the week".

His remarks were in reply to Labour's Keir Starmer, who asked: "What an embarrassment - the last 24 hours have given a new meaning to the phrase 'coalition of chaos'. 

"Yesterday the rubber hit the road. Fantasy has hit reality.

"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?"

The shadow Brexit minister also blasted the DUP as "wagging the tail of the Tory dog" after Brexit talks were left in tatters over the Irish border yesterday. 

Mr Davis told MPs the issue of maintaining "a frictionless border between the UK and Ireland" will be dealt with in the next phase of negotiations. 

Meanwhile, Tory MPs also praised the DUP for ensuring Mrs May stuck to the “Brexit red lines”.

Backbencher Jacob Rees-Mogg said:  "Does my right honorable friend share my gratitude to the DUP for helping the government stick to its own red lines?"

On a dramatic day in Brussels, Mrs May and Mr Juncker were involved in an extraordinary row over the future of the Irish border ahead of a crunch deadline next week. 

Mrs May seemed on the verge of negotiating a deal which would move Brexit talks forward to trade before the DUP made a furious intervention. 

The Shadow Secretary of State for Brexit was granted an urgent question following questions in the Chambers this afternoon, where he said: "What an embarrassment, this is a coalition of chaos" after Theresa May and Jean-Claude Juncker reached a stalemate over the Irish border on Monday. 

Mr Starmer said "this is deeply serious" and asked Brexit negotiator David Davis "what kind of message is Theresa May sending to the EU?" after she buckled to pressure from the Unionist party. 

He added: "The DUP tail is wagging the Tory dog."

DUP leader Arlene Foster refused to accept any terms which would see Northern Ireland leave the EU on different terms to the rest of the UK after Mrs May proposed aligning the state with the Republic. 

But standing side by side in Brussels following the end of yesterday's session, the Prime Minister and EU bureaucrat both insisted their talks had been "constructive" and had made progress.

A spokesman for the European Commission said all eyes are now on London.

They said: “The show is now in London. We stand ready for talks with the UK at any time when London is ready.

“We will not discuss any texts that have not been agreed and which have not been seen by the College of Commissioners.”