Boris Johnson has said he has a “solution” to the Brexit impasse which he will shortly present to European Union leaders in the hope of securing a withdrawal deal by the 31 October deadline.

But the prime minister distanced himself from reports that the UK’s plan involves a string of “customs clearance areas” five to 10 miles away from the Irish border to avoid the need for checkpoints on the dividing line between Northern Ireland and the Republic.

The proposal was instantly dismissed as a “non-starter” by Dublin when it surfaced in reports on Monday night.

But Mr Johnson said that the idea did not feature in the “proposals we are actually going to be tabling”, but was an option put on the table by the UK earlier in negotiations.

The PM declined to set out details of the UK’s proposed withdrawal agreement which he is expected to present at the end of this week, in the hope of securing EU assent at a crunch Brussels summit on 17 October and avoiding having to request an extension to negotiations two days later.

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He told BBC1’s Breakfast: “We do have a solution, and there is a very good way forward.

“But what is required now is for everybody to come together to look at it and to think how can we best progress this, for people, for businesses, for communities on both sides of the border and for the whole of the UK economy.

“Our solution, I think, will do all that.”

He made clear he will be appealing directly to national capitals as well as the EU institutions in Brussels, saying: I very much hope the Europeans, our EU friends in Brussels, in Dublin, in Germany as well, want to take it forward.”

Mr Johnson said the UK was reaching “the moment when the rubber hits the road… when the hard yards really are in the course of the negotiations”.

He rejected suggestions that his plan was little more than a relabelled version of Theresa May’s thrice-rejected withdrawal agreement.

“There’s no there’s no point in doing Brexit if you stay locked to the customs union, you stay locked in the single market with no say on those institutions, no say on that rule-making,” he said.

“And that was basically what the the existing withdrawal agreement committed this country to do. That is why it’s essential to come out of the backstop.

“The most important thing is that we bust out of the so-called backstop arrangements, which keep the UK locked in Brussels’ customs union, commercial trade policy, and regulatory affairs, all the laws that come from Brussels.

“Under the backstop, we would have to accept a huge proportion of them without any say in the making of those rules. What we’re doing by abolishing the backstop is coming out taking the freedoms that are so vital for Brexit.”

Mr Johnson did not rule out encouraging European leader to refuse to delay Brexit – as a way to circumvent anti no-deal legislation – but denied having made such a request.

“We haven’t,” he told the BBC. “In truth, we have not made any such request.

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“My own view is that they want to get this done as much as we do and indeed the majority of the British public do, whether they voted for leave or remain.”

It comes after The Times reported that Mr Johnson’s plan to get around the Benn Act would be to ask EU leaders to rule out any extension to the October 31 deadline.

He would then seek to present MPs in parliament with a straight choice of agreeing the revised deal or leaving without an agreement on Halloween.

In reference to Downing Street source comments that Remain MPs should be investigated for “foreign collusion”, Mr Johnson said there was a “legitimate question to be asked” about legislation from emergency debates in parliament.

“I think there is a legitimate question to be asked about the generation of this SO24 legislation,” he said.

“It is a very interesting situation. We have bills and an act – the so-called Surrender Act – that I’m afraid has a massive consequence for the people and economy of this country were it to be effected.