Mr Davis will be accompanied by a nine-strong negotiating team that includes the most senior civil servants at the department as well as officials from the Treasury and Home Office as well as Mark Sedwill, the national security adviser to the Prime Minister. At a meeting of European Union foreign ministers in Luxembourg he said: "The most important thing for us is to look to the horizon, raise our eyes to the horizon".
"We must first tackle the uncertainties caused by Brexit - first for citizens but also for the beneficiaries of the European Union policies and for the impact on borders, in particular Ireland", Barnier told reporters at the start of the talks.
Davis, a prominent tough-talking figure in the "Leave" campaign, sounded a positive note too, saying "there is more that unites us than divides us".
"As we enter into the most important negotiations that our country will embark on in our lifetimes, the economy must be front and centre ..."
Even though May triggered the two-year process on March 29, negotiators will have to get a full agreement much faster than March 2019.
Prime Minister Theresa May has repeatedly insisted the Government is prepared to walk away from the talks, claiming no deal is better than a bad deal.
Ms May's government is reeling from a crisis of her own making: the loss of her parliamentary majority in a June 8 snap election she did not need to call.
International Trade Minister Liam Fox will travel to Washington on Monday to explore new trade ties - although no formal negotiations are possible until Britain has actually left the bloc.More news: Health care plan endangers poor
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 first round of formal negotiations on Britain's withdrawal from the European Union will begin on June 19, it has been confirmed.
Speaking to BBC Radio 4's Today Programme, he said: "It has to be a practical solution, I think 90 per cent of MPs have been voted in on a pro-Brexit ticket so it's just a question really of what the technique is and what the bargaining position is".
The others have ruled out letting May negotiate in person with German Chancellor Angela Merkel, French President Emmanuel Macron and others.
Anxious by immigration and loss of sovereignty, Britain a year ago voted to end its decades-old membership of the 28-country bloc - the first state ever to do so - in a shock referendum result.
While Barnier insists on the "sequencing" of talks, so that trade negotiations can not start until probably January, finding a way to avoid a "hard" customs border for troubled Northern Ireland may well involve some earlier discussion of the matter.
The leader of Britain's House of Commons said the state opening will take place on June 21st.
And what about the questions about her government's handling of two issues unrelated to Brexit: terror attacks and the deadly Grenfell tower block fire?
May has been under pressure since the election cost her her majority to consider "softer" Brexit options than the clean break she proposed from the EU single market and customs union.