Mr Fox ruled out any delay to full European Union withdrawal that prevented Britain from signing trade deals with non-EU countries from day one after departure day, in March 2019.
The worldwide trade secretary, Liam Fox, played down the idea of divisions between him and Hammond over the length of any post-Brexit transitional deal with the European Union, which he has talked of in terms of months, while the chancellor has said it could be in place for years.
Finance minister Philip Hammond, who like May campaigned last year to keep Britain in the European Union, said on Sunday he believed most of his Cabinet colleagues now backed the idea of having two years or more of a transition period after Brexit in March 2019 - to soften the disruptive effect on society and the economy.
They then left the podiums without answering any questions from the fathering media, with the Frenchman saying the pair needed to work to which the Brexit secretary replied: "Work, yes that's right - work". In particular, the delegations are expected to focus on how to manage new border arrangements, what rights EU and United Kingdom citizens will hold post-Brexit and, most controversially, how much London owes the Union.
The EU has demonstrated increasing confidence in recent weeks, accusing Britain of dithering over whether it wants a "hard" or "soft" Brexit more than a year after the shock referendum that propelled May to power.
'We made a good start last month, and this week we'll be getting into the real substance, ' he said.
Davis is expected to call for both sides to "get down to business" as he arrives for the second round.
'Protecting the rights of all our citizens is the priority for me going into this round and I'm clear that it's something we must make real progress on'.
And his allies blasted Michael Gove for reportedly being behind the "smear campaign" of leaking details from last week's Cabinet meeting. Mr Hammond all but admitted a report he had told the cabinet that public-sector workers are "overpaid" was true - while denying he had said "even a woman" can drive a train.
Barnier said: "We will now delve into the heart of the matter".
"I think on many fronts it would be helpful if my colleagues - all of us - focused on the job in hand".
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 negotiations can move on to discuss a future trade deal later this year.
"The plenary meetings [of the Brexit talks] will show us whether there is a realistic basis for agreement or whether the British government can not move at all because of its own problems", said Elmar Brok, a German centre-right MEP who helps coordinate the European parliament's position on Brexit.