Boris Johnson demands immediate start of stage two Brexit negotiations

But Mr Johnson said that the difficult issue of customs controls on movements between Northern Ireland and the Republic could only be resolved in the context of wider negotiations on the EU’s post-Brexit relationship with the UK.

The EU says that trade talks can begin only after “sufficient progress” has been made on the three key divorce issues of citizens’ rights, the Irish border and the UK’s financial settlement.

And Dublin has warned that unless the UK provides cast-iron guarantees that the border will remain open, it will not allow Brexit negotiations moving on to the second phase – including trade talks – before the end of the year.

The Democratic Unionists – who prop up the Government in Parliament – have insisted they will not sign up to any proposal for Northern Ireland to remain in “regulatory alignment” with the Republic once Britain has left the EU.

Meanwhile reports suggest that Hard Brexiteers within Mrs May’s Cabinet have voiced opposition to her signing Britain up to any deal which would stop it diverging from EU regulations on issues like food safety, environmental protection and workplace rights after Brexit.

Speaking to reporters as he arrived for a Nato summit in Brussels, Mr Johnson said: “We will come up with a solution but the important thing is that that solution can only be discovered in the context of discussions on the end-state of the UK’s relations with the rest of the EU.

“We need to get on with those negotiations now, so all the more reason to get on with stage two of the negotiations.

“What I would say is that the best way to sort it out is to get on to the second phase of the negotiations, where all these difficult issues can be properly teased out, thrashed out and solved.”

In a clear sign that he was not budging from the Hard Brexit demands of his Vote Leave campaign, Mr Johnson said: “I think the important thing is that what we are going to do, as the Prime Minister has repeatedly said, is we are going to take back control of our borders, of our laws and UK cash contributions. That’s the way forward.”

Mrs May had expected to speak with DUP leader Arlene Foster yesterday in an attempt to resolve their differences but – in a possible sign of how intractable the issue has become – the call did not take place. It is not clear when they will next talk.

Mrs Foster has complained that her party was only shown the proposed text late on Monday morning, around the time the prime minister was sitting down to lunch in Brussels with European Commission president Jean-Claude Juncker.

Mrs May insisted the talks in Brussels had made “good progress” and that she would be returning to the Belgian capital later in the week with a view to finalising an agreement on the terms of Britain’s withdrawal.

Meanwhile some Conservative Hard Brexiteers said she should be prepared to walk away from the negotiating table altogether if the EU refused to allow the negotiations to move on.

Former cabinet minister and hardcore Brexiteer Iain Duncan Smith suggested the point was approaching “fairly fast” unless the EU was prepared to adopt a different course.

“We cannot go to trade arrangements at any price because that price will be paid in the sense of the kind of arrangement that we end up with that could be wholly intolerable,” he told the BBC.

Shadow Brexit secretary Sir Keir Starmer reiterated that Labour was prepared to keep membership of the single market and customs union up for negotiation following a transition period after withdrawal.

He told BBC Radio 4’s Today programme: “We say leave that option on the table. We certainly wouldn’t rule it out. We’d want to have a conversation.

“We are in the EU and we will leave the EU; the question then is, can we reach an agreement with the EU that gives us those benefits?”

Sir Keir said Norway’s deal with the EU was the nearest model for the UK, but a British version would need to be different.

He said the government had got itself into a “contorted position” on the Northern Ireland border issue, and that a UK-wide agreement was needed.

Progress in the Brexit talks was on the agenda at a meeting of the EU commissioners, including Mr Juncker, in Brussels.