Secretary of State for Exiting the EU David Davis described the talks as a mission to deliver on the will of the British people following the referendum of a year ago. They are due to give a joint news conference after talks among their teams lasting seven hours. Both sides want transparency to be the default.
Barnier hailed that the first session was "important", "open", and "useful indeed to start off on the right foot as the clock is ticking". "And use the time in between to work on proposals and exchange them".
The talks are set to kick off at 11 a.m. (0900 GMT) in Brussels with a meeting between Davis and the EU's chief Brexit negotiator Michel Barnier.
Still, British Foreign Secretary Boris Johnson remained upbeat Monday, saying he thinks the negotiations will yield "a happy resolution that can be done with profit and honor for both sides".
"To that end, we are starting negotiations in a positive and constructive tone, determined to build a strong and special partnership between ourselves and our European partners and friends in the future", he said.
European Union leaders have said they hope sufficient progress is made on the key divorce issues by the autumn to allow discussions to begin on the future trade and security relationship.
"It was confirmed yesterday that the United Kingdom meant to leave the single market and leave the customs union".
The groups, which claim to represent hundreds of thousands of businesses across the United Kingdom employing millions of people, have also called for a "frictionless" open border between Ireland and Northern Ireland.
Davis brushed off a suggestion that a weakened Conservative government had dropped objections to a Brussels timetable, which would deal first with European Union priorities, including its demand Britain settle a "Brexit bill", and leave the talks on free trade that May wants until at least late this year.
Britain's political instability has caused concerns in European capitals hoping to get the negotiations over with quickly and cleanly, as has May's oft-repeated threat to walk away from the talks without a deal if necessary.
Regarding one of the key sticking points of any future agreement, British Prime Minister Theresa May is set to make a proposal on the issue of European Union citizens' rights in Britain at an European Union summit this week, he said.
The two sides agreed to set up three working groups covering the details of withdrawal: the financial settlement; citizens' rights; and one dealing with other legal issues relating to "separation". Agreeing to pay a "Brexit bill" may be more inflammatory.
But he insisted preserving the Good Friday Agreement and Common Travel Area is a "majority priority" for Brussels during negotations.
This is a stark retreat from Davis' core demands before the talks, where he had called for parallel talks on both aspects of the process.
Hammond may also give more details of his budget plans after saying on Sunday that he was "not deaf" to the weariness of voters to almost a decade of spending cuts for many services and tight controls on public sector pay.
When 52 percent of British voters opted for Brexit, some feared for the survival of a Union battered by the euro crisis and divided in its response to chaotic immigration.
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