"We must first tackle the uncertainties caused by Brexit", centering on citizens living on each other's territory, border arrangements between Ireland and the United Kingdom and the amount that Britain stands to pay to get out of its previous European Union commitments, Barnier said.
These include the issues of Britain's estimated €100 billion (S$175 billion) exit bill, the rights of European Union citizens living in Britain, and the fate of the border in Northern Ireland. A day after the start of Brexit talks, Hammond sought to soften the more confrontational tone towards the bloc taken by Prime Minister Theresa May - a role he has re-adopted since her election flop earlier this month.
"Tory David Davis has crumbled on the very first day of Brexit negotiations, as he was forced to agree to the EU's timetable", wrote the Daily Mirror, a left-leaning tabloid.
Chancellor of the Exchequer Philip Hammond said on Friday that protecting jobs and the British economy would be priorities for his country. Both sides will put top advisers to work immediately on a border agreement between Ireland and the United Kingdom, aiming to make sure the Irish peace agreement and the common travel area should as unaffected by Britain's European Union departure as possible.
Mr Hammond described the talks as a "positive start", but warned it "will get tougher".
After an initial exchange of diplomatic pleasantries, Barnier took advantage of Davis' weaker position, and seven hours of negotiations lead to the United Kingdom backing down on all fronts.
Germany's Europe minister, Michael Roth, said in Luxembourg that the opening of the negotiations had shown British leaders still needed a "reality check" on what they could achieve.
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"Before long, we will all begin to find out the extent to which Brexit is a gentle stroll along a smooth path to a land of cake and consumption", Carney said at the annual Mansion House event, which was postponed from last week by a deadly fire in a London tower block.
The chancellor emphasized the importance of the UK's financial sector to the European Union and warned against any disruption to it.
Meanwhile, German Chancellor Angela Merkel yesterday urged the EU's remaining 27 members to stick together during the Brexit talks.
"In order to work on this subject we need to be enlightened more on the nature of future relations which obviously will have repercussions for the content and the dimensions of such transition periods", Barnier said.
"I would like us to get a good agreement that is in both sides' interests".
It also appears Mr Davis and Mr Michel Barnier may have to negotiate in the dark as staff have been told to switch off all the lights.
Most of the attention will be paid to the negotiations on the future relationship with Ireland.