Theresa May and her senior ministers have discussed the possibility of a second referendum on Brexit as part of talks with Labour to break the deadlock and avoid crashing out of the EU.

The negotiations, which will continue today, included the scenario that the option of a confirmatory referendum could be put to MPs in a series of votes next week.

Following the meeting, Labour leader Jeremy Corbyn sent a note saying: “Agenda items were customs arrangements, single market alignment including rights and protections... internal security, legal underpinning to any agreements and confirmatory vote.”

However, government sources later played down the suggestion any concrete deal had been reached on the issue.

The Prime Minister will also shortly write to Donald Tusk, President of the EU Council, requesting an Article 50 extension.

But this has sparked a potential rebellion from Brexiters within her own ranks.

She faces the threat of further high-profile resignations if she is intent on seeking a long delay to the Brexit process.

Yesterday evening, following four-and-a-half hours of talks, Mrs May met with an inner circle of senior ministers to take stock of the inter-party discussions, with a suggestion that a run-off vote on various Brexit options should include a confirmatory referendum on any agreed deal.

Those present at the meeting in No 10 were thought to include Philip Hammond, the Chancellor, David Lidington, the Prime Minister’s de facto deputy, Stephen Barclay, the Brexit Secretary and Michael Gove, the Environment Secretary, as well as Geoffrey Cox, the Attorney General.

It came after Irish Prime Minister Leo Varadkar warned the UK must produce a “credible and realistic way forward” to have a chance of getting a further delay to Brexit.

EU leaders like Mr Varadkar and German Chancellor Angela Merkel have made it clear they need to see a concrete proposal from Britain to justify putting off exit day for another period of time – but that they want to avoid a no-deal Brexit.

“Matters continue to play out in London and we need to be patient and understanding of the predicament that they are in,” the Irish Prime Minister acknowledged.

Yet he added: “But of course, any further extension must require and must have a credible and realistic way forward.”

At present, that does not exist. Following talks in Dublin with Mr Varadkar Ms Merkel insisted: “Until the very last hour – I can say this from the German side – we will do everything to prevent a no-deal Brexit.

“We will simply have to be able to do this. “We have to be successful and we hope for a solution that we can agree with Britain.

“I heard that you have the same saying as what we say in Germany: ‘Where there’s a will, there’s a way.’”

Mrs May has made clear she will seek a further extension beyond the rescheduled exit day of April 12 when she travels to Brussels next Wednesday for a special EU summit.

Back in London, the Conservative and Labour talks in the Cabinet Office between Mrs May and Mr Corbyn’s teams were “productive”, said No 10, but it was reticent about giving away any details about subject matter discussed or any progress made.

It said both sides hoped to meet again today “for further work to find a way forward to deliver on the referendum, mindful of the need to make progress ahead of the forthcoming European Council”.

Labour was even more tight-lipped, saying only that the talks had taken place, they were continuing and the “teams are planning to meet again”.

On Tuesday, when the PM made her announcement to “break the logjam”, she said that if the Conservative-Labour talks failed to agree on a single unified approach, she would offer a run-off vote between a number of options for the future relationship.

Crucially, Mrs May made clear the Government would abide by the Commons’ decision but, to make the process work, so too would the Opposition.

Since UK ministers failed to lay a parliamentary motion yesterday, this means there will be no Brexit run-off vote on Monday, should the talks break down.

Given Donald Tusk, the European Council President, has made clear he needs as much advance warning as possible ahead of Wednesday’s summit, then it seems clear any run-off vote would take place on Tuesday.

However, Downing Street said it was a matter for the EU27 to determine “what they are seeking from the UK”, but the expectation was they would want “clarity on the way forward in the UK Parliament on how we are going to ratify the deal and exit the EU as soon as possible”.

Asked if “clarity” meant a Commons vote, the PM’s spokesman referred back to Mrs May’s statement earlier in the week, adding: “I am genuinely not in a position to say definitively what the position will be on Tuesday.”

Senior Government insiders posited the possibility that the PM could go to Brussels next week while talks with Labour were continuing without any votes having taken place.

Yet this would raise doubts about whether the EU27 would be willing to offer any extension in such circumstances.

Earlier, Mr Barclay, in a warning echoed by Downing St, told MPs the bill promoted by Labour’s Yvette Cooper, designed to stop the UK crashing out of the EU next week, had created the danger of an “accidental no-deal Brexit”.

The Brexit Secretary claimed the measure could backfire if the Commons rejected any Brexit delay offered by EU leaders at next Wednesday’s summit as there would be no time to renegotiate it before the deadline for departure two days later on Friday.

In other developments:

*The Commons was suspended for the day after a torrent of water descended into the chamber as MPs rambled on, not about the merits or demerits of Brexit, but about that other scintillating topic, the Loan Charge; a move to counter tax dodging.

*Downing Street announced six ministerial replacements for those who resigned over the Government’s Brexit policy. Among them is James Cleverley, the Tory Deputy Chairman, who becomes a junior minister at the Department for Exiting the EU.