Government talks with Labour on a compromise Brexit deal will continue after “productive” technical discussions.
Ministers and their Labour counterparts held a second round of talks on Thursday amid the continuing crisis at Westminster.
Both sides said they planned to meet again on Friday in their bid to reach a breakthrough over the UK’s departure from the EU.
The prime minister hopes to secure a further delay to Brexit, by again extending the Article 50 negotiating period, at a summit of EU leaders next Wednesday.
However, Theresa May will have to present a proposal to Brussels as to how she will break the deadlock in the House of Commons, where MPs have rejected her Brexit deal three times but also failed to back any alternative outcome.
On his way into Thursday’s talks at the Cabinet Office, Labour shadow Brexit secretary Sir Keir Starmer revealed the idea of a “confirmatory” referendum on any agreement was among the issues his party wanted to discuss.
The subject of a fresh public vote was also at the centre of a cabinet clash after Chancellor Philip Hammond described it as a “perfectly credible proposition”.
His remarks were dismissed by a string of fellow ministers.
Following the conclusion of the latest round of discussions with Labour, a Downing Street spokesman said: “Today both sets of negotiating teams met for four-and-a-half hours of detailed and productive technical talks in the Cabinet Office, supported by the civil service.
“The government and the Opposition hope to meet again tomorrow 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.”
The government was represented by Mrs May’s deputy David Lidington, Brexit Secretary Stephen Barclay, chief whip Julian Smith and Number 10 chief of staff Gavin Barwell.
Sir Keir and shadow business secretary Rebecca Long-Bailey were joined at the talks by party officials.
Meanwhile, German Chancellor Angela Merkel met with Irish Prime Minister Leo Varadkar in Dublin on Thursday.
Ms Merkel vowed her country would “do everything” to prevent a no-deal Brexit on 12 April, the current Brexit deadline, until “the very last hour”.
She said: “We do hope that the intensive discussions that are ongoing in London will lead to a situation by next Wednesday, when we have a special council meeting, where Prime Minister Theresa May will have something to table to us on the basis of which we can continue to talk.”
Ms Merkel added: “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 together with Britain.”
Mr Varadkar reiterated the EU’s stance that any further Article 50 extension must be accompanied by a “credible and realistic way forward” from the UK government.
He said: “Matters continue to play out in London and I think we need to be patient and understanding of the predicament that they are in.”
The Irish premier also restated that the EU is prepared to amend the political declaration on its future relationship with the UK if Mrs May’s red lines shift.
Labour have demanded the government negotiate a post-Brexit customs union with the EU, but the prime minister is under pressure not to accept the opposition’s position from a large number of her own MPs.
In an interview with Sky News, Defence Secretary Gavin Williamson failed to say whether he would accept membership of a customs union in order to strike a deal with Labour.
He said: “The House of Commons has a choice. It has a choice of accepting a deal that doesn’t include the customs union, is able to deliver Britain’s exit from the EU swiftly, and I very much hope it takes the opportunity to do that.
“But, of course, the prime minister quite is rightly talking across the political spectrum to ensure Britain exits the EU in the time as swiftly as everyone wishes to see it.”
Labour leader Jeremy Corbyn, who was present alongside Mrs May at the first round of cross-party Brexit talks on Wednesday, is also facing competing pressures on how to approach the talks.
Despite a large part of his party backing a second EU referendum, a group of 25 MPs wrote to him on Thursday to urge him not to demand a confirmatory public vote in the discussions with the government.
Late on Thursday, the prime minister appointed Tory deputy chair James Cleverly as a Brexit minister to replace Chris Heaton-Harris, who resigned earlier this week in protest at Mrs May’s decision to seek a further delay to the UK’s exit from the EU.
Kevin Foster was also appointed to the Wales Office to replace Nigel Adams, who quit the government over the prime minister’s shift to negotiating with Labour over a Brexit deal.