European leaders have ramped up the pressure on Theresa May to change course on Brexit after she told them her Chequers plan was the only route to a deal.

The Prime Minister insisted the UK’s March 29 2019 departure from the European Union would not be delayed, and with time running short the onus was on the bloc’s leaders to find a solution – or face the prospect of a no-deal scenario.

But Mrs May faced calls to hold a second referendum amid warnings about the risk of a no-deal Brexit as leaders gathered in Salzburg to discuss the EU’s next move in the negotiations.

With the issue of how to avoid a hard border between the UK and Ireland after Brexit still to be resolved, Taoiseach Leo Varadkar said “time is running short” to reach a deal.

Maltese prime minister Joseph Muscat has said there is “almost unanimous” support among EU leaders for Britain to hold a second referendum on membership of the union.

On BBC Radio 4’s Today he said any deal would be “sub-optimal” to continued membership and “it won’t be as easy as yesterday to trade between the two sides”.

Czech prime minister Andrej Babis said: “We hope that finally we will reach a deal but basically I am very unhappy that the UK is leaving, so it would be better maybe to make another referendum and maybe the people in the meantime could change their view.”

Luxembourg’s prime minister Xavier Bettel said: “I know that the Chequers plan is something that was not easy for Theresa May to pass through in her own Government.

“I am convinced that we will find an agreement, but time is getting short. We both need to find a compromise.”

The Netherlands’ Mark Rutte said: “As long as there is no deal, there is the risk of ‘no-deal’.”

The Prime Minister set out her plans over dinner with her EU counterparts on Wednesday night.

Theresa May in conversation with Luxembourg's Xavier Bettel in Salzburg (Matthias Schrader/AP)
Theresa May in conversation with Luxembourg’s Xavier Bettel in Salzburg (Matthias Schrader/AP)

European Commission president Jean-Claude Juncker said the presentation was “interesting”, adding: “It was polite, it was not aggressive, she was doing her job.”

Mrs May said Chequers was “the only credible and negotiable plan on the table that delivers no hard border in Northern Ireland and also delivers on the vote of the British people”.

She added: “If we are going to achieve a successful conclusion then, just as the UK has evolved its position, the EU will need to evolve its position, too.”

UK Government sources revealed that Mrs May used Wednesday night’s dinner to acknowledge the difficulties and that she had “never pretended Brexit would be easy or simple”.

She made clear the high stakes of the negotiations over the coming weeks if a deal is to be struck this autumn in time for ratification by March next year.

Despite the comments from Mr Muscat and Mr Babis, the Prime Minister showed no intention of giving ground on the issue of a so-called People’s Vote when asked about it at the summit on Wednesday.

“I want to be absolutely clear – this Government will never accept a second referendum,” she said.

Thursday’s agenda in Salzburg involves the leaders discussing internal security matters before talks over lunch – in Mrs May’s absence – about Brexit.

The Prime Minister’s domestic difficulties over Brexit also continued, with criticism from a senior Tory and a call from Scotland’s First Minister Nicola Sturgeon to delay the UK’s departure from the EU.

Sir Mike Penning, a former defence minister who voted Leave before backing Mrs May for the party leadership, told the Telegraph she had treated Tory MPs “like children who belong on the naughty step”.

The former soldier told the paper he was joining the hardline Brexiteer European Research Group (ERG), saying: “I’ve come to the conclusion that this ‘put up, shut up’ attitude of the Prime Minister’s – ‘it’s Chequers or nothing, you do as you’re told or else’ – is a massive insult, not only to my colleagues but also to the voters.

“She is playing a game of Russian Roulette with the country which is frankly an insult to the referendum result and all those people who voted, no matter how they voted.”

Ms Sturgeon has written to opposition leaders at Westminster arguing that if the UK fails to agree a deal with the EU, the timetable for talks must be extended.

“If the choice we face is between no deal and no detail, then an extension to the Article 50 negotiation period must be on the table as the only way to avoid an economic cliff edge, and allow all alternative options to be considered,” she said.