The EU Council boss stressed the need for further offers from the British side, particularly on Ireland, following a meeting with Theresa May in Brussels this evening. 

Leaving the Eastern Partnership Summit the prime minister admitted there are “still various issues” that need to be solved between the two parties but said they “still want to move forward together”.

Mr Tusk said: “Sufficient progress in the Brexit talks at December EU Council is possible. But still a huge challenge. We need to see progress from UK within 10 days on all issues, including on Ireland.” 

Exiting the summit tonight Mrs May said the two sides are still making “progress” on the key issues but offered no new details about the two major sticking points. 

On Ireland she said the UK Government is committed to “ensure movement of people and trade across the border can continue as it is now” - a promise unlikely to satisfy Dublin. 

And on the thorny Brexit bill she pointed once more to the pledge in her Florence speech that the UK will “honour its commitments” but did not address rumours she is upping the amount on the table to £40 billion. 

Mrs May said: "There are still issues across the various matters that we are negotiating on to be resolved, but there’s been a very positive atmosphere in the talks and a genuine feeling that we want to move forward together.”

“We have been making progress and we are making progress throughout these negotiations across all of the issues that we are still addressing. In relation to the border between Northern Ireland and the Republic of Ireland we and the Irish government continue to talk about the solutions for that. 

“We have the same desire. We want to ensure that movement of people and trade across that border can carry on as now and that we don’t create any new barriers to trade or the movement of people across that border. That’s the outcome that we have both agreed on. And that is what we believe it is in the best interest of Northern Ireland." 

On the the Brexit bill, Mrs May confirmed that she had discussed the issue with Mr Tusk amid rumours she had agreed Cabinet consent to up her offer to £40 billion in a bid to unblock the talks. 

She said: “We have been talking about how we can progress the issue in relation to the financial settlement. I‘ve set out the position. I did so in the Florence speech. I said that we would honour our commitments. 

“I said that no country, no member state of the European Union need worry that would receive less or have to pay more in the current budget plan and that we would honour our commitments. And that’s what we’ve been talking about." 

EU diplomats described the meeting as "like the first step in a seven step tango" and have not ruled out a final round of negotiations being squeezed in between now and next month's summit. 

Earlier in the day Mr Tusk risked angering eurosceptics as he implied that Russia had interfered in the Brexit referendum by misquoting a speech given by the PM. 

Earlier today the Bulgarian prime minister broke ranks with his fellow EU leaders to warn that the divorce talks are heading towards a break down for which Europe is hopelessly unprepared. 

Boyko Borisov said it was his “sentiment” that the divorce talks will crash and burn, adding that anyone who believes the EU can easily brush aside such a setback is “overestimating” the club. 

In a series of unguarded remarks, Mr Borisov warned his fellow EU leaders of the dire consequences they face if they do not manage to achieve a good trade settlement with the UK. 

He told Euractiv: “Regrettably, this possibility is more and more mentioned, that there would be no agreement. I am not saying it on behalf of the EU or of our presidency, and I don’t want to be misunderstood.”