Davis, a veteran Eurosceptic, told Barnier that his team aimed to maintain a “positive and constructive tone” during the talks.
One diplomat said Ms May tried to “hijack” the summit by drawing other leaders into Brexit talks, though European Union officials played down suggestions of any agenda row with London. The talks must be completed and endorsed by parliaments by the end of March 2019.
Monday’s negotiations are to open at 11:00am in Brussels (0900 GMT) with 90 minutes of talks between Barnier and Davis, followed by a working lunch between the pair and a press conference.
“While there will undoubtedly be challenging times ahead of us in the negotiations we will do all that we can to ensure that we deliver a deal that works in the best interests of all citizens”.
The start of the negotiations comes as work continues across the British government to prepare Britain for life outside of the EU.
The two representatives for the Britain and EU, David Davis and Michel Barnier respectively, have exchanged mountaineering gifts and sat down to begin ironing out a plan that includes topics like trade agreements and citizenship claims.
The EU says it will not compromise on its core “four freedoms”: free movement of goods, capital, services and workers.
Three key issues will dominate the first phase of the talks.
She said: “During the election I was very clear on the idea of a hard Brexit where we lost out on access to the single market and protection for the rights of Europeans here and our residents”. Aware that this is a priority for the EU, May is reportedly set to make a “generous offer” on the issue early in the talks.
Last year’s Brexit 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.
After Davis and Barnier met over lunch in the Commission’s top floor dining rooms, their teams broke up into “working groups” that will be charged with handling specific areas of talks that the European Union expects to take place for a week every month.
Both sides have said settling the question of whether European Union citizens living in the United Kingdom, and British expats in European Union countries, will have the right to remain after Brexit is a top priority. 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.
May has said she is open to some kind of association agreement with the customs union and wants to avoid any so-called “cliff-edge” into uncertain trading conditions, but she has also said Britain must be able to control immigration – something it can not do while a member of the EU. Speculation has also mounted that she could now seek a softer Brexit, which involves staying in either the EU’s single market or customs union.
“The best way we can spend this week is to rebuild trust”, rather than tackle the big hard issues right at the start, another European source said. Agreeing to pay a “Brexit bill” may be more inflammatory. A fair deal for both sides was possible, he said.
Prompted by her poor election showing, particularly among pro-EU young people who fear losses of jobs and opportunity from Brexit, some of her most senior ministers and two former Conservative prime ministers have called for a rethink.