In carefully choreographed talks that even saw the two men exchange mountaineering gifts, they agreed to discuss divorce issues before negotiations on a future trade deal can start.
"Davis said the row of the summer would be over the sequencing of Brexit talks, and one day in he has capitulated", he said.
Chancellor of the Exchequer Philip Hammond and Bank of England Governor Mark Carney joined forces to fight against the fragmentation of financial services after Brexit as the government seeks to shift its focus away from controlling migration to safeguarding jobs.
Finance minister Philip Hammond and Bank of England governor Mark Carney stressed the perils of an abrupt divorce from Britain's biggest trading market, seeming to contradict some of the "hard Brexit" rhetoric espoused by the government at the start of negotiations with the European Union on Monday. But it must be done in a way that works for Britain ... However, Hammond made a point of acknowledging the concerns of other European Union countries about their oversight of financial markets which are vital to their economies but will be outside the bloc.
Adding to the complexity is Britain's current political situation, as May lost her Conservative majority in parliament after a snap election, sparking wide criticism of her leadership and worries about how long May and her cabinet would stay in power.
She should also listen to young people, who had shown in the last general election that they wanted good jobs, he said.
In the first step, the two sides will deal with "the most pressing issues" in order to "lift the uncertainty caused by Brexit", including "citizen rights, the single financial settlement, and other separation issues".
Davis's agreement to Monday's agenda led some European Union officials to believe that May's government may at last coming around to Brussels' view of how negotiations should be run.
Jean Claude-Juncker, the President of the European Commission, told Prime Minister Theresa May that "Brexit can not be a success" at a dinner at Downing Street in April, commenting that Britain will not even be in the Customs Union.
European Union officials had earlier warned May not to make that offer so early in the talks. "A deal like no other in history", Davis said in a statement as he headed into the talks.
"I would like us to get a good agreement that is in both sides' interests".
"Today we agreed on dates, we agreed on organization, and we agreed on priorities for the negotiation", he said, outlining a two-step negotiation.
"It was clear from the opening that both of us want to achieve the best possible outcome and the strongest possible partnership". Agreeing to pay a "Brexit bill" may be more inflammatory.