German federal elections could see Angela Merkel replaced as Chancellor by former European Parliament president and staunch federalist Martin Schulz, who once called for the creation of a "genuine European government".
Theresa May has said she is "getting on with the job" amid continued questions over her future as Prime Minister.
Davis is to meet Michel Barnier, the EU's chief Brexit negotiator, to kick off hugely complex withdrawal negotiations that are expected to conclude within two years.
Meanwhile, according to reports the Brexit negotiations may be a very dry affair.
Davis, a prominent tough-talking figure in the "Leave" campaign, sounded a positive note too, saying "there is more that unites us than divides us". We keep hearing that they don't want a 'Norway model, ' they don't want a 'Swiss model, ' they want to leave the customs union, the internal market, they want to limit migration. The general election earlier this month - called abruptly by Prime Minister Theresa May to bolster her majority and show a united Brexit face to Brussels - backfired spectacularly, and cost her Tories dearly.
Trade talks between the United Kingdom and European Union will not begin until October at the earliest as Brexit negotiations will follow the timetable set out by Brussels in a blow to David Davis. He added: "Brexit won't make anything better, but it will make a lot of things more hard".
Working groups will be set up to focus on three key areas - the status of EU citizens living in Britain and British citizens living in the EU; the divorce bill for Britain; and the future of the Northern Irish border with EU member Ireland.More news: Father's Day creator was Renaissance woman, descendant says
Oxfordshire MPs have also set out their positions on Brexit, with the newly elected MP for Oxford West and Abingdon has vowed to "fight for her constituents" and oppose a hard Brexit in European Union negotiations which start today.
Mr Davis warned: "These talks will be hard at points but we will be approaching them in a constructive way". International Trade Minister Liam Fox will travel to Washington on June 19 to explore new trade ties - although no formal negotiations are possible until Britain has actually left the bloc. Looking more sombre than his British counterpart, he said he hoped they could agree a format and timetable on Monday.
"And we agreed that we stand a much greater chance of success if our teams work together as that's been demonstrated today". But both diplomats underlined that any future partnership with the European Union would bring responsibilities as well as benefits.
"We need back control of our borders, we will leave the single market and the customs union." he said. He added that Britain would have to accept the jurisdiction of either the European Court of Justice or a "joint court" of Europeans and Britons.
Brexit department mandarin Olly Robbins and the UK's ambassador to the EU, Sir Tim Barrow, will join Mr Davis for the lunch session.
The smiles belied the fact that at stake is not just Britain's future but also Europe's postwar political order and its place in the world, which could be fatally undermined without an agreement by the March 2019 deadline.
Hammond may go some way to soften that and could find an unlikely ally in Brexit minister David Davis, whose earlier criticism of businesses for hiring foreigners has also troubled companies.