THERESA May remains wedded to her Brexit plan despite being told it “will not work” at a summit of European Union leaders, setting up a tense month of negotiations as time runs out to reach a deal.

The Prime Minister said the Chequers blueprint is the only proposal on the table as the deadline approaches, with the next leaders’ meeting in October set to be a “moment of truth”.

READ MORE: Nicola Sturgeon says Brexit talks must be extended if necessary

But May indicated the UK will unveil new measures on the future status of the Northern Irish border in a bid to break the deadlock.

Speaking at the end of a two-day EU summit in Austria – during which she had a meeting with Irish counterpart Leo Varadkar – May said the UK will “shortly” come forward with new proposals on the so-called “backstop” arrangements for implementation at the border if no long-term solution is found.

May, who also held “frank” face-to-face talks with European Council president Donald Tusk at the informal Salzburg summit, insisted Chequers is the “only serious and credible proposition” for an overall deal. But Tusk said the 27 other EU leaders had agreed the plans need to be redrawn.

Individual leaders of EU nations were equally blunt. German chancellor Angela Merkel said “substantial progress” is needed over the next four weeks, while French president Emmanuel Macron said leaders of the Brexit campaign who told British voters it would be easy were “liars” and leaving the EU was “not without costs”.

The next major milestone in the Brexit process is fast approaching, with the October 18 summit labelled a “moment of truth” by Tusk.

An additional Brexit summit could be held in November, but only if a deal is within reach.

Tusk said: “In October we expect maximum progress and results in the Brexit talks and then we will decide whether conditions are there to call an extra summit in November to finalise and formalise the deal.”

At a news conference at the conclusion of the summit, May struck a defiant tone, saying she had always expected negotiating “tactics” to be used during the course of the Brexit process.

She has flatly rejected a European Commission backstop proposal for Northern Ireland to remain within the EU customs area after Brexit, arguing this would draw a border down the Irish Sea.

Speaking after her meeting with Tusk, the PM said: “We both agree there can be no withdrawal agreement without a legally-operative backstop. But that backstop cannot divide the United Kingdom into two customs territories, and we will be bringing forward our own proposals shortly.

“On the economic partnership, there is no solution that will resolve the Northern Ireland border which is not based on the frictionless movement of goods.

“Our White Paper remains the only serious and credible proposition on the table for achieving that objective.”

With the Chequers plan facing resistance from the EU and a bitterly divided Conservative Party, a no-deal Brexit remains a potential outcome.

May said: “Let nobody be in any doubt: as I have always said, we are preparing for no deal, so that if we get to the position where it’s not possible to reach a deal then the British people can be confident that we will have done what is necessary to ensure we make a success of leaving the EU, regardless of the terms on which we do so.”

Tusk insisted despite the EU’s reservations about Chequers, he is “a little more optimistic” about the prospect of a “positive outcome”.

But he added “unfortunately we cannot at this stage exclude a no-deal – it depends on both sides of negotiations”.

Jacob Rees-Mogg, leader of the influential European Research Group of pro-Brexit Conservatives and a prominent critic of the Prime Minister’s plan, summed up events in Salzburg by tweeting “Chequers goes pop” with the hashtag #ChuckChequers.

Shadow Brexit secretary Sir Keir Starmer weighed in, saying: “It has been clear for weeks that Theresa May’s Chequers proposals cannot deliver the comprehensive plan we need to protect jobs, the economy and avoid a hard border in Northern Ireland.”