EFFORTS to get a Brexit deal should “accelerate” in the coming months, Theresa May and Jean-Claude Juncker have said in a joint statement but the Prime Minister’s desired breakthrough on starting trade talks remained elusive.

After a 90-minute dinner at the EU’s headquarters in Brussels, which involved a “broad, constructive exchange on current European and global challenges,” Mrs May emerged to give the European Commission President a kiss while David Davis, the Brexit Secretary, made his farewell with a bear-hug for Mr Juncker.

Before the meal, the PM had a telephone conversation with Emmanuel Macron, the French President, in an apparent effort to get him to soften his line on Britain promising to stump up tens of billions of euros on the divorce settlement before any talks could even begin on a future trading relationship with the EU27.

Downing Street said the two leaders had "discussed progress" in the negotiations and agreed to go over the "next steps" in the margins of the EU summit later this week.

Having spoken to Angela Merkel, the German Chancellor, about trade and transition over the weekend, it seems Mrs May was left in no doubt that the Franco-German alliance remained determined to play hardball and would not budge on sequencing.

French officials made clear Paris and Berlin were “perfectly aligned” in their approach to Brexit.

Ahead of the working dinner, Mr Juncker caused wry smiles when he said he would give a “post-mortem” after the meal had finished.

In their joint statement he and the PM said it had taken place in a “constructive and friendly atmosphere”.

It went on: “As regards the Article 50 negotiations, both sides agreed that these issues are being discussed in the framework agreed between the EU27 and the United Kingdom, as set out in Article 50 of the Treaty on European Union.

“The Prime Minister and the President of the European Commission reviewed the progress made in the Article 50 negotiations so far and agreed that these efforts should accelerate over the months to come.”

The working dinner, which according to Downing Street, had been planned for weeks took Westminster-watchers by surprise; it was not mentioned in Mr Juncker’s pre-released diary last week.

David Mundell, after a meeting of the intergovernmental Joint Ministerial Committee in Whitehall, brushed aside the notion that Mrs May was panicking over Brexit.

He said: “I completely dismiss that. It’s appropriate that the PM engage in the discussion; she has always been clear she would directly engage in the discussions.”

He went on: “It is, of course, incumbent on the Government to prepare for no deal. We can’t control whether there’s a deal; there are 27 other parties in this negotiation. But we are not planning or preparing to have no deal. We want there to be a deal but it would be wrong not to take steps to plan for that contingency.”

But Michael Russell, the Scottish Government’s Brexit minister, who had also attended the JMC, expressed extreme concern over the possibility of not getting an agreement, telling reporters: “The prospect of having no deal is utterly unacceptable and would be disastrous for Scotland...disastrous for the whole of these islands.”

Later this week, Mrs May will be at the regular European Council, which is expected to discuss immigration, counter-terrorism and the Iran nuclear deal.

There might well be an opportunity for the PM to raise Brexit on the sidelines while the EU27 are likely to discuss the Brussels talks, minus the UK, when they will confirm that insufficient progress has been made to move onto the second phase of negotiations about trade. Mrs May is also expected to hold her usual post-summit press conference on Friday.

In April, details about a previous private dinner at Number 10 were leaked when Mr Juncker was reported to have famously said that he had he left Downing Street "10 times more sceptical" than when he had arrived.

The leak led to an angry response from Mrs May on the steps of Downing Street when she warned that "there are some in Brussels who do not want these talks to succeed".