Theresa May will attempt to sell her Chequers plan directly to fellow European Union leaders as she calls for Brussels to compromise as the clock ticks down to Brexit.

The Prime Minister will use a gathering of EU leaders in Salzburg to say the UK’s position has “evolved” with the publication of her proposals, and now it is time for Brussels to follow suit.

On the eve of the informal meeting of EU heads of government, Brussels’ chief negotiator Michel Barnier said he was ready to come forward with a new offer on the Irish border.

He said he was working on an “improved” plan to avoid the return of a hard border while respecting the territorial integrity of the UK, in an attempt to break the deadlock.

But he warned that time for an agreement was running out and the “moment of truth” would come at the next full EU summit on October 18.

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Michel Barnier has said he is ready to make an improved offer on the Irish border (Niall Carson/PA)

“It is then we shall see whether agreement we are hoping for is in our grasp,” he told a news conference.

The gathering in Salzburg will be the first time EU leaders have met since Mrs May published her Chequers blueprint for Brexit in July.

Over dinner at the Felsenreitschule – the theatre where the Von Trapp family performed before fleeing the Nazis in The Sound Of Music movie – Mrs May will set out her plan and explain why Brussels should show more flexibility to give her the support she needs.

In an interview with the Daily Express she said it was the “right plan” for the UK while representing a “good deal for the EU”.

“I’m not going to be pushed away from doing what is necessary to get the right deal for Britain,” she said.

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(PA Graphics)

Mrs May is expected to use the Salzburg summit to hold formal face-to-face talks with Belgian premier Charles Michel on Wednesday and Ireland’s Leo Varadkar and European Council president Donald Tusk on Thursday.

She may talk to other leaders in the margins of the summit in an effort to win backing for a plan which has met fierce resistance from within the ranks of her own Conservative Party.

As part of the drive to set out the UK’s position to the EU’s leaders, Mrs May used an article in German newspaper Die Welt to explain her stance.

“A lot has been said about what the UK is asking for, so I want people to hear directly from me about what I am trying to achieve and the motivation behind it,” she said.

The Chequers blueprint – a “common rulebook” for trade in goods and “business-friendly facilitated customs arrangement” – is the only way to resolve the thorny issue of the border between Northern Ireland and Ireland, she said.

“It is profoundly in both sides’ economic interest, it respects the integrity of the single market and, crucially, no one else has come up with a proposal that could command cross-community support in Northern Ireland that is the only true foundation for stability there.”

The Government argues Brussels’ plan, which would see Northern Ireland remain in the customs union until a new arrangement could be agreed, would effectively create a border between the North and the rest of the UK – something the Prime Minister has said she could not accept.

Mrs May said: “To come to a successful conclusion, just as the UK has evolved its position, the EU will need to do the same.

“Neither side can demand the unacceptable of the other, such as an external customs border between different parts of the United Kingdom – which no other country would accept if they were in the same situation – or the UK seeking the rights of EU membership without the obligations.”

Mr Barnier said his latest proposal to break the deadlock would “de-dramatise” the controls that would be necessary in the event of the backstop coming into play.

“We are clarifying which goods arriving in Northern Ireland from the rest of the UK would need to be checked and where, when and by whom these checks could be performed,” he said.

“We can also clarify that most checks can take place away from the border at the company premises or in the markets.”

Mr Barnier made clear that time to reach a deal was running out with his comment that the next summit on October 18 would be a crucial stage in the process.

Attention had been increasingly focused on the prospect of a special summit in November to finalise an agreement, but Mr Barnier said it should be clear before then whether a deal was possible.

European Council president Donald Tusk said EU leaders should discuss arrangements for the “final phase” of the Brexit talks “including the possibility of calling another European Council in November”.

In a letter to leaders ahead of the Salzburg meeting he called on them to work on “limiting the damage” caused by Brexit.

“Unfortunately, a no-deal scenario is still quite possible. But if we all act responsibly, we can avoid a catastrophe,” he said.