In addition, unidentified sources told The Times that Hammond would urge the government to rethink its plan to leave the trade group, which guarantees tariff-free trade with other members but bans trade deals with third parties.
European Union negotiator Michel Barnier said the negotiations which should lead to a breakup by March 2019 "must first tackle the uncertainties caused by Brexit - first for citizens, but also for the beneficiaries of the European Union policies and for the impact on borders, in particular Ireland".
Davis's agreement to Monday's agenda led some European Union officials to believe that May's government may at last coming around to Brussels' view of how negotiations should be run.
European Union diplomats hope this first meeting and a summit in Brussels later this week, where May will be present but will not negotiate with European Union leaders, can improve the atmosphere after recent spiky comments from both sides.
British Prime Minister Theresa May will later meet Angela Merkel, Emmanuel Macron and other EU leaders at the European Council summit. 'Put the economy first'They point out that their organisations represent hundreds of thousands of businesses across the United Kingdom, employing millions of people, and say the business community fully accepts the voters' decision in last year's referendum to leave the EU.
Mr Barnier has said talks on a trade deal can not even start until sufficient progress has been made on the other issues.
But the situation is very different from 12 months ago when the Brexiteers were riding high, with Prime Minister Theresa May's entire approach called into question after a disastrous election performance on June 8.
Davis gave Brussels' chief negotiator a book on mountaineering - an account of a French expedition to the Himalayas - while Barnier presented Davis with a traditional carved wood hiking stick from his home region of Savoie. The move backfired, May lost her Conservative majority in the vote and has been fending off critics of her leadership ever since. "I think on balance it has weakened our hand as a country having such a close election", he said.
Protection of the benefits of free trade agreements now delivered through the EU. The Irish issue, long described as a priority for both, will be treated somewhat differently; avoiding a "hard border" will necessarily have to take account of how the rest of EU-UK trade will work. He said he hoped for a "soft Brexit", which would leave many trade and immigration ties in place.
The start of the negotiations comes as work continues across the British government to prepare Britain for life outside of the EU.
In a position paper published earlier this month, the European Union said it wants broad rights for citizens of the European Union and Britain, as well as their families.
Davis said that the two sides already have similar positions.
Germany's deputy foreign minister, Michael Roth, told RBB Inforadio that "we must of course protect our interests as the European Union 27 but naturally we also don't want to punish Britain".
John Kampfner, CEO of the Creative Industries Federation, a national organization for the creative industries and the arts, said that the election outcome means that "there is no clear mandate for the government to negotiate a hard Brexit".
Talks will begin at 0900 GMT with a joint press conference by former French foreign minister and European commissioner Barnier and Davis at around 1630 GMT. I am determined." Davis channelled Winston Churchill: "The pessimist see difficulty in every opportunity, the optimist sees opportunity in every difficulty. "I am certainly a determined optimist".