The UK plans to continue participating in the single market - which allows frictionless trade and the free movement of people between European Union members - during the transition phase, before the final trading relationship, which has yet to be negotiated, comes into force.
"The benefits of a transitional period go beyond the need for time to deal effectively with these operational issues, but the latter are nonetheless important", he said, before adding, "We think this is an important safeguard and a sensible way to underpin financial stability". Her eagerness to keep them onside was underlined late Sunday when her office said the United Kingdom would leave the bloc's customs union after the divorce, acceding to a key demand of the Brexit hardliners.
"This approach involves utilising the UK's existing tried and trusted third country processes for UK-EU trade, building on EU and worldwide precedents, and developing new innovative facilitations to deliver as frictionless a customs border as possible", the paper said.
A senior government source says the prime minister wants to "put this to rest".
He met May at Downing Street before his official talks with Davis, following which he told reporters that the two sides had agreed to move on to the next phase of Brexit negotiations.
He said that is now being worked on, describing it as "significant" that the latest talks are about the withdrawal agreement rather than a trade deal.
A spokesperson for the prime minister added on Monday that the government was instead looking at agreeing either a "highly streamlined customs arrangement" or "a new customs partnership" with the EU.
Today, negotiators will press for a transition agreement to be confirmed by the EU Council summit in March in a bid to provide certainty to businesses and investors.
What Downing Street has not said is what prime Minister proposes instead of " or "a" customs union.
But business leaders have urged the UK Government to remain in a customs union, and Tory remainer Anna Soubry urged Number 10 to "do the maths" and listen to company bosses.
It will be followed by meetings of the Cabinet's Brexit sub-committee on Wednesday and Thursday. Some ministers believe the country could remain in the customs union for a year or two longer, until new infrastructure is built at ports and before any new global trade deals are ready for implementation.
Mrs May has made clear she will resist European Union proposals for these people to be entitled to settle permanently in the UK.
The lunch of David Davis and Michel Barnier, accompanied by ir respective teams closest, is anteroom of first official round of negotiations, after having reached in December an agreement on terms of divorce, which will begin tomorrow in Brussels. People will be free to live and work here.
While the country - and Brussels - wait for May to outline her ideas for Britain's relationship with its biggest trading partner, the void has been filled by feuding cabinet ministers setting out vastly differing visions of the future.