Asked if he had made any concessions to the United Kingdom in exchange, Barnier said the talks were not about "punishment" or "revenge" and the two sides had to simply accept the "responsibility and the consequences" that came with their decisions.
But in Britain many media portrayed Davis, a veteran Brexit campaigner, as having climbed down from his insistence that the European Union must immediately open talks on a future free trade agreement rather than limit negotiations, as they are now, to basic issues of the divorce, such as the rights of expatriate citizens.
"Because membership of the single market requires the four freedoms [of people, goods, services and capital] to be abided, and [because] we need to bring back to Britain control of our laws, control of our borders, we'll be leaving the single market", he said.
TRT World's Simon McGregor-Wood reports. But the impact of the depreciation doesn't last long and credit ratings agency DBRS says that whatever the shape of the Brexit deal, uncertainty "is likely to adversely impact the economy and the fiscal accounts".
Mr Hammond also said Britain would nearly certainly need an implementation period on its exit from the EU's single market and its Customs union.
"When the British people voted last June, they did not vote to become poorer, or less secure", Hammond said Tuesday.
The vote came as a profound shock to Brussels against a backdrop of rising anti-EU sentiment, with many - including now US President Donald Trump - predicting the bloc's eventual break-up.
May is eight seats short of a majority in Britain's parliament amid increasingly evident cracks in her own party just as crucial Brexit negotiations get under way.
In an apparent reference to UK Ministers" repeated insistence that "no deal is better than a bad deal', M. Barnier said: "For both the European Union and the UK a fair deal is possible and far better than no deal".
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In choreographed talks that saw the two men exchange mountaineering gifts, they agreed to discuss divorce issues before negotiations on a future trade deal can start. They are due to give a joint news conference after talks among their teams lasting seven hours.
Attending her first European Council Summit since her disastrous general election, it is understood the Prime Minister will explain the UK's "principles" on the issue of citizens' rights - a key early topic in the Brexit negotiations.
Solving the vexed question of keeping the peace and an open border between the British province of Northern Ireland and the Irish Republic - an European Union member - will be an urgent priority in the talks, Mr Barnier and Mr Davis agreed.
"The best way we can spend this week is to rebuild trust", rather than tackle the big hard issues right at the start, a European source said.
Populist politicians in Austria, the Netherlands and France who had a lukewarm attachment to the European Union at best, failed to make the headway they may have anticipated in recent elections, while German Chancellor Angela Merkel is widely expected to win again in elections this autumn.
Finally, they want to ensure that the 1998 Good Friday peace agreement between Ireland, and European Union member, and Northern Ireland, which is part of Britain, is not put in jeopardy.
"We will of course implement what Britain pitches, but in a way that the interests of the 27 member states are safeguarded".
Macron, a committed pro-EU leader and ally of Merkel, also easily won French legislative elections on Sunday, cementing his power base. The discussions come at a time when the United Kingdom government is in a minority position in the Commons and will be reliant on the support of the Democratic Unionist Party to gain a slender overall majority of two.
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