THERESA May has been given a 10-day deadline to come up with proposals on the Irish border, the “divorce bill” and citizens’ rights that will satisfy EU leaders – otherwise Brexit talks cannot move on to discussing a future trade deal.

The Prime Minister was given the ultimatum by Donald Tusk, the European Council president, at a meeting in Brussels yesterday afternoon.

It came at the end of a difficult week for the UK Government in which it became apparent the remaining EU countries were fully behind member state Ireland on not budging on its demands for no hard border.

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Tusk posted an update on social media after the meeting saying that while progress was still possible, it would be a “huge challenge”.

“Sufficient progress in #Brexit talks at December #EUCO is possible. But still a huge challenge. We need to see progress from UK within 10 days on all issues, including on Ireland,” he tweeted late yesterday afternoon.

After the same meeting May conceded “issues” still had to be resolved but insisted progress had been made and that there had been a “very positive atmosphere”.

Speaking in Brussels, May did not answer specific questions about the financial settlement and said there were “still issues across the various matters that we’re negotiating on to be resolved”.

But she added: “There’s been a very positive atmosphere in the talks and a genuine feeling that we want to move forward together.”

The UK, she said, would honour its financial commitments and shared the same desire as Ireland to stop barriers to trade or movement across the border.

May had lunch with German Chancellor Angela Merkel before meeting with Tusk.

Merkel told May last week that she has until the start of December to make an enhanced offer on the financial settlement and provide guarantees on the Irish border after Brexit.

Ministers have given their backing to increase the UK’s “divorce bill”, reportedly from £20 billion to £40bn, but only if the EU shows movement on trade.

Tusk had previously signalled the EU was “ready” to move on to the next phase of talks at the EU summit on December 14 – to focus on a trade and security partnership after the UK leaves in March 2019 – but only if the UK shows progress on outstanding issues.

Danish PM Lars Lokke Rasmussen told journalists in the Belgian capital that there had been “movement” on the issue of money.

“It seems to me that there is progress and so I have decided to be optimistic about this,” Rasmussen – one of the UK’s closest allies – said.

Earlier yesterday Downing Street signalled it was ready for discussions regarding whether Northern Ireland could remain in the EU customs union, a move which would help facilitate a soft border post-Brexit, saying it was “a matter for negotiations”.

Dublin is pushing hard for written assurances from London that there will be no “hard border” between Northern Ireland and the Republic, warning that deadlock in Brexit negotiations cannot be broken until the issue is resolved.

With the UK committed to withdrawing from the customs union and the single market, Irish foreign minister Simon Coveney said yesterday it was difficult to see how border checks could be avoided if it resulted in “regulatory divergence” between Northern Ireland and the Republic.

Taoiseach Leo Varadkar has suggested a “bespoke” arrangement similar to that operated on the Isle of Man, under which Northern Ireland, or the whole of the UK, continues to observe the rules of the single market and customs union without remaining a member of them.

However, DUP leader Arlene Foster warned against any divergence between the regulatory framework of Northern Ireland and Britain.

“What we don’t want ... is any perception that Northern Ireland is in any way different from the rest of the UK, because that will cause us great difficulties in relation to trade. The single market that really matters to us is the single market of the United Kingdom.”

She accused the Irish Government of “using the negotiations in Europe to put forward their views on what they believe the island of Ireland should look like in the future”.

Asked at a regular Westminster media briefing yesterday whether Northern Ireland could remain in the customs union following Brexit, a Downing Street spokesman said: “That is a matter for negotiations.

“Our position on Northern Ireland has been set out in the papers and we need to continue to negotiate to find an innovative way forward.”

Downing Street declined to comment on a report which suggested Brexiteer Michael Gove believes he has secured May’s commitment to insist on the UK diverging from EU “regulatory harmonisation” after withdrawal – which could raise the likelihood of a no-deal Brexit.