Over three and a half days, the two sides will hold detailed discussions on all aspects of the divorce treaty: protecting citizens' rights, money, and the Irish border.
They want to frustrate Brexit.
When Britain leaves the European Union on 29 March 2019, Brussels wants to ensure that individuals and companies do not fall into a legal black hole where goods in transit fail to reach their intended destination and ongoing British court cases at the ECJ can not conclude.
The Brexit Secretary said progress had to be made this month on a deal for reciprocal rights for citizens.
One unnamed Cabinet minister was reported have hit back, claiming Mr Hammond was part of an attempt by "the Establishment" to prevent Britain ever leaving the EU.
Mr Davis is facing strong opposition from the EU over Britain's proposals for rights of European nationals living in the United Kingdom, as well as pressure to accept paying a huge "divorce" bill.More news: Call of Duty: WWII Zombies' trailer has leaked, developers not happy
Crucially, last month, Mr Davis caved in to the EU's insistence that the talks would move on to trade only when "enough progress" had been made on Brussels' three priorities.
The Brexit secretary said he would be "getting into the real substance" of the separation but he might end up speaking more about unity after the chancellor, Philip Hammond, complained on Sunday that he was being briefed against by fellow ministers opposed to his pro-business approach.
He said he came under attack at the weekend from hard line Brexiteers "who are not happy with (my) agenda" after a series of cabinet leaks meant to undermine him.
"I do think on many fronts it would be helpful if my colleagues - all of us - focused on the job at hand", he told the BBC. These two key players will meet regularly through the week, with the aim of keeping the talks on track.
British officials recently have also brought up the idea a transitional period after the March 2019 deadline to avoid a "cliff edge" scenario when it leaves the European Union, although the length and details have yet to be determined.
On that timetable, Barnier reckons, a broad political deal on the outlines of a new, open trading relationship could be in place by late next year, allowing for a transitional phase of up to a few years after Brexit to negotiate all the details.