Top-level talks aimed at finding a way out of the Brexit deadlock will continue between the UK Government and Labour today.

The discussions are taking place as Prime Minister Theresa May faces a week of hectic diplomacy as she battles to keep her EU withdrawal agenda on track.

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European Council president Donald Tusk waves at the European Parliament in Strasbourg, France. Picture: AP Photo/Jean-Francois Badias

The dialogue with Labour comes amid reports EU officials are considering offering the PM a flexible extension – or “flextension” – to the Article 50 timetable.

Mr Tusk is preparing to put the option to EU leaders at a crunch summit next Wednesday in a bid to prevent the UK crashing out of the bloc on 12 April, according to the BBC.

His plan would allow the UK to leave sooner if Parliament ratifies a deal, but it would need to be agreed by EU leaders.

As Government talks with Labour on EU withdrawal went into another day, the issue of a new Brexit referendum continued to be a focus of attention.

Ministers have considered the possibility of giving MPs a vote on holding a referendum on a deal as part of the talks with Labour, the Daily Telegraph reported.

It is understood the Government could set out proposals to Labour leader Jeremy Corbyn in a letter today.

And Mrs May faced a continued challenge to her authority from Parliament as the House of Lords debated a Bill aimed at extending the Brexit process in a bid to avoid a no-deal scenario.

The remaining stages of the European Union Withdrawal (No.5) Bill will be considered by peers on Monday, threatening a new political headache for the PM if it is approved.

The bill, brought forward by backbenchers including Labour’s Yvette Cooper, allows Parliament to determine the length of any Brexit extension the Prime Minister should request at the EU summit on 10 April.

If the European Council proposes a different extension, Mrs May would be required to return to the Commons to obtain MPs’ approval.

Attorney General Geoffrey Cox said the Bill would leave the PM with little room to manoeuvre.

Referring to the Bill’s impact on a no-deal option, the Attorney General told the BBC: “It rules it out ... the Prime Minister would have little choice but to accept the extension that she’s offered.”

Mr Cox said if the talks with Labour failed there would be repercussions.

He said: “The problem, then, would be that we would be in an extension. It’s likely to be a long one, by which I mean longer than just a few weeks or months.”

Labour MP Siobhain McDonagh predicted a number of her colleagues could quit the party over the issue of a new referendum.

Ms McDonagh told the BBC: “There is going to be outrage if we don’t get a second vote.

“Would it be the thing that made me leave the party? I don’t think so, there are other issues for me.

“But, would it make some of my colleagues in the parliamentary Labour Party? Yes, a number have said to me that would be the moment that they would leave.”

However, a number of Labour MPs representing Leave areas have come out against the idea of a confirmatory referendum.

Mrs May will be expected to spell out the UK’s plans in a letter to Mr Tusk in sufficient time for the other 27 leaders to consider them before they gather in Brussels for the summit.

Talks between the Government and Labour lasted four-and-a-half hours on Thursday.

David Lidington, effectively the deputy prime minister, led the Government’s negotiating team with Brexit Secretary Steve Barclay, Chief Whip Julian Smith, Business Secretary Greg Clark and Theresa May’s chief of staff Gavin Barwell.

On the other side of the table were shadow Brexit secretary Sir Keir Starmer and shadow business secretary Rebecca Long-Bailey along with senior Labour officials.

Labour’s victor in the Newport West by-election, Ruth Jones, said she is against a no-deal exit from the EU.

Brexit: Donald Tusk suggests ‘flexible’ 12-month delay for UK