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Tusk, the president of the council of European Union heads of states and governments, said the bloc was now again starting to be perceived as a solution, rather the problem, and that recent difficulties had served to strengthen it.

In all instances, the Taoiseach has relayed Ireland's position in securing a Brexit deal that has the least damaging effects for the Irish economy and political stability.

The two-day Brussels summit will predominately focus on counter-terrorism, common defence and security.

Theresa May will be present for the first part of the meeting where she'll update her counterparts on the forming of the new United Kingdom government and try to allay some of the anxieties over Brexit in particular in the area of citizens rights.

"I hate Brexit from every angle", Dutch Prime Minister Mark Rutte said of stopping a move Britons voted for previous year.

His upbeat assessment follows a series of election setbacks for populist and eurosceptic parties, including French far-right leader Marine Le Pen who lost heavily to newcomer Macron in last month's presidential poll.

It was her first foray into the Brexit talks, one which was timed to coincide with coffee at the end of dinner by European Union leaders who have warned the British prime minister not to use Council summits as a negotiating chamber for Britain's departure.

"The PM will give an update to the other member states on the UK's Brexit plans following the beginning of the negotiations this week", a Downing Street spokesman said. "I am NOT a dreamer and I'm not the only one", Michel told reporters as he arrived at the summit, reflecting the Brussels consensus that Britain is definitely leaving and that talk of a U-turn, which would need European Union consent, is simply a waste of time.

"So who knows? You may say I am a dreamer but I'm not the only one", Tusk continued, quoting a lyric from the late John Lennon's "Imagine".

Foreign Secretary Boris Johnson said he hoped leaders of the 27 other nations would match her "generous" proposals with similar offers to the one million British expats on the continent.

Brexit talks kicked off on Monday, and the EU's chief negotiator, Michel Barnier, will brief European Union leaders after May has left the room on Thursday night.

Ahead of private talks with May Thursday, Tusk said he had been asked by British friends if he could see a way of Britain still staying in. "We today don't have a British government declaration on the direction that's to be taken" on Brexit, "so we're in a very, very hard situation", he said.

He said that "we are working hand in hand with Germany" and that the two countries, the historic twin-driving motors of European integration, plan "to speak with one voice".

On Monday, a report by Automotive Council UK found that 44% of all components used in UK vehicle assembly come from British suppliers, compared with 41% in 2015, highlighting a move by manufacturers to protect themselves from Brexit-related disruptions to their supply chain.