About a month after their first meeting, the two intend to push forward with a detailed plan that could minimize economic and social damage to both Britain and the European Union after Brexit.
Working groups will focus on three areas: citizens' rights; the EU demand that Britain pays some 60 billion euros ($69 billion) to cover ongoing EU budget commitments; and other loose ends, such as what happens to British goods in EU shops on Brexit Day.
Barnier has warned the United Kingdom that the time is running out. "The clock is ticking", he said once again last Wednesday.
Last week, the United Kingdom acknowledged for the first time it will have to pay a contribution upon leaving.
The U.K. tried to allay those concerns on Thursday with a written statement to Parliament referring explicitly to a "financial settlement" for the first time. Asked point blank on Monday if the cabinet was "split on Brexit", Johnson simply said he was pleased negotiations had begun and then defended the offer May has made to protect the rights of European Union citizens in Britain.
We're not going to be talking a couple of months, we are going to be talking a couple of years.
During four days of talks the two sides hope to make progress on key issues surrounding Britain's withdrawal, including citizens' rights and its exit bill, so that talks can move on to discuss a future trade deal later this year.
That is a daunting task, especially that the United Kingdom government, marred by infighting, has been slow to draw up its own Brexit plan, has no clear tactic, and have lost political capital at the ballot boxes in June.
One unnamed Cabinet minister was reported to have hit back, claiming Mr Hammond was part of an attempt by "the Establishment" to prevent Britain ever leaving the EU.
The meeting takes place against a backdrop of bitter feuding among United Kingdom ministers over the Brexit strategy.
"Five weeks ago, the idea of a transition period was quite a new concept, I think now you would find that pretty much everybody around the cabinet table accepts that there will be some kind of transition", he said. Failure to conclude Brexit negotiations by March 30, 2019 would create huge uncertainty for businesses and millions of people across Europe.