Here is the latest from our Correspondent James Crisp:

European Council President Donald Tusk was asked after the summit if Mrs May’s goal of finalising a Brexit agreement by October was possible.

That deadline was also set by Michel Barnier, the European Union’s chief negotiator, to allow time for it to be ratified by governments and MEPs.

“It is still realistic but dramatically difficult,” the former prime minister of Poland said, “the second phase will be more demanding, more challenging than the first phase.”

Jean-Claude Juncker, the president of the European Commission, said: “The real negotiations on the second phase will begin in March next year.”

The next step would be for the commission to turn yesterday’s negotiating guidelines into initial terms of the transition agreement, which would then be negotiated by Britain.

But Mr Tusk revealed that “exploratory contacts” with the British over the UK vision for the future partnership, which includes a trade deal, would start now rather than the March.

The Telegraph understands the UK is keen to begin negotiations on trade and transition at the same time and as quickly as possible.

A Whitehall source said: ‘Both sides agreed that once sufficient progress was met talks about the future partnership and its implementation would commence so today is a good step forward.

“The Council have repeatedly said there’ll be discussions about the future partnership before March and we will hold them to that. There’s no question of backsliding and we won’t let the more glacial elements of the Commission to use these guidelines as an excuse to freeze up.’

German Chancellor Angela Merkel said she would not have voted for Brexit but admitted “significant progress” had been made. Like Mr Tusk, she warned that the hard work started now.

“The most difficult phase is ahead of us. It is very complicated and complex,” she said. “The good news is that all 27 member states, so far, have put in tremendous efforts and have stuck together.”

One EU source described the discussion by EU-27 leaders as “very short and Very sober”. The text granting “sufficient progress” was adopted in 10 minutes, according to the source.