For Britain, it's a role reversal, having been buoyed by strong growth in recent times - even after the momentous vote on June 23, 2016 to leave the EU.
The EU is not so keen, as it seems to think this offers it some leverage over the UK.
From his comments, it appeared that the Brexit talks will largely follow the EU's conditions and will center on the two sides' new relationship only once sufficient progress has been made on the withdrawal issues.
Mrs May will this evening set out a proposal on the rights of European Union citizens living in Britain, and will brief other leaders on the political situation in the UK.
Leaders had agreed with summit chair Donald Tusk not to open discussions with May and she left immediately afterwards, leaving the other 27 to discuss other Brexit issues without her.
"The British public have rejected the Tory extreme hard Brexit".
Theresa May made a "fair and serious offer" to European Union leaders over the contentious issue of the future rights of EU citizens, offering those who arrive lawfully before Brexit the chance to build up the same rights to work, healthcare and benefits as United Kingdom citizens.
She would also offer any European Union citizen resident for five years - at some cut-off date - the opportunity to get settled status, a new category which would treat them as if they were British citizens for healthcare, education, benefits and pensions.
Britain's Prime Minister Theresa May failed spectacularly to achieve a majority for her Conservative Party in the general election she called for earlier this month, undermining confidence in her ability to remain in the top job.
At their first meeting in Brussels on Monday, British and European Union negotiators agreed on a timetable for the Brexit talks.
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But, even with the softer tone and expressed eagerness to sort out one of the relatively easy problems that the Brexit talks will have to unpick, there were bound to be sticking points.
Martin Schulz, the Social Democrat (SPD) chancellor candidate who Merkel will square up against in her bid to win a fourth term in September's election, told the same conference: "The best result of the Brexit negotiations would be - there wouldn't be a Brexit".
David Davis began negotiations yesterday. "I look forward to working closely with you during this negotiation", EU negotiator Barnier said, as quoted by the press service of the European Commission, the EU's executive. We must lift the uncertainty caused by Brexit.
"It is crucially important now that we know what Great Britain wants from Brexit".
May's proposals at an European Union summit were a carefully timed gesture days after talks began on Britain's departure.
"But at the same time, I am a realist and this is why first of all we should start our negotiations as effectively as possible. The protection of the Good Friday agreement and the maintenance of the Common Travel Area are the most urgent issues to discuss", the European Union negotiator explained.
"We will of course implement what Britain pitches, but in a way that the interests of the 27 member states are safeguarded".
Mr Varadkar is expected to raise the Paris Climate Agreement, security, as well as economic and trade issues.
Davies denied suggestions the agreed timetable showed Britain's "weakness" and insisted it was "completely consistent" with the government's aim of parallel trade and exit talks.
"It's not how it starts, it's how it finishes that matters".