Mr Barnier said that Britain and the European Union have agreed on the priorities and timetable for Brexit negotiations after the first session of talks. The appointment of both senior officials to the Irish portfolio was a measure of how centrally the sides saw the issue, according to Mr Davis and Mr Barnier.
Davis, answering a question, said Britain's negotiating position had not changed as a result of his Conservative Party's poor showing in recent elections.
"We're in the same place, we take the same view as Michel [Barnier] on this, we want to see the public informed... by proactive publication of what we are doing, not by leaks or erroneous briefings", Davis said. An early election this month, in which British Prime Minister Theresa May lost her Conservative majority in parliament, only added to the problems.
Days after a suggestion from French President Emmanuel Macron that Britain could still choose to remain, Davis said there would be no backtracking from Prime Minister Theresa May's plan to deliver on Brexit, for which Britons voted in a referendum nearly a year ago.
Anxious by mass immigration and loss of sovereignty, Britain previous year voted to end its decades-old membership of the 28-nation bloc in a shock referendum result. For the officials sitting down on Monday, at least on the European Union side, a major worry is Britain crashing out into a limbo, with no deal.
A spokesman for the Department for Exiting the European Union said: "We believe that the withdrawal process can not be concluded without the future relationship also being taken into account". "That is why we will work all the time with the United Kingdom, and never against the United Kingdom".
Those issues are the exit bill; the rights of three million European Union nationals living in Britain and the one million Britons on the continent who now are allowed to live, work and claim welfare benefits; and the status of the border between Northern Ireland and Ireland. The EU insists that should wait until an outline agreement on divorce terms, ideally by the end of this year.
Only once the EU27 determine that "sufficient progress" has been made on these issues will talks be able to progress to a second phase, where the two sides will begin to scope out the future of their relationship.
After the initial shock of last year's Brexit vote and faced with rising anti-EU sentiment, the bloc at 27 appears to have steadied in recent months and got a real boost with the election of new French President Emmanuel Macron in May.
"I would like us to get a good agreement that is in both sides' interests".
But he said that Monday morning's terror attack in London and the devastating fires in Portugal reminded him that "there is more that unites us than divides us".
Barnier has warned that the negotiations must be wrapped up by October 2018 to allow time for all parties to ratify a final accord by March 2019.