The officials will be addressing several issues like the rights of British citizens in the European Union and vice versa, how much money will be owed by Britain and how to minimize split effects on the fragile peace between Ireland and Northern Ireland.
Davis, a veteran campaigner against European Union membership, said he sought quick and substantive progress in what is scheduled to be a two-year negotiation before Britain leaves the EU.
Brexit secretary David Davis agreed to drop earlier demands he made last week that trade talks should run in parallel with the divorce discussions, an issue that he had promised to turn into "the row of the summer".
Uncertainty surrounding the outcome of the Brexit talks - such as the possibility that Britain crashes out of the European Union with no deal - is also likely to make consumers cautious.
At the same time, while it was a priority, he said, to show progress in averting difficulties for troubled Northern Ireland as a result of being on a new EU-UK border, agreement on how the border would work would depend on wider future trade ties.
Regarding the future relationship with the EU, Davis said Britain has not changed its position, reiterating that Britain will leave the single market and the customs union, which is "the only way" to allow Britain to develop free trade agreements with non-EU countries.
"When the British people voted last June, they did not vote to become poorer, or less secure", Hammond said Tuesday.
British Prime Minister Theresa May is due to praise the good atmosphere at Monday's Brexit talks, and explain how to protect the rights of citizens hit by Britain's departure.
Adding to the complexity is Britain's current political situation, as May lost her Conservative majority in parliament after a snap election, sparking wide criticism of her leadership and worries about how long May and her cabinet would stay in power.
Ricciardo wins chaotic Azerbaijan GP; Vettel, Hamilton clash
Nothing happened did it...he brake checked me as well so what do you expect? "I don't run into the back of him on goal ". Further chaos unfolded when Daniil Kvyat stopped, his Toro Rosso having lost all electrical power on lap eight.
Nearly exactly a year after Britain's seismic referendum to leave the bloc, the EU's chief negotiator, Michel Barnier of France, welcomed his counterpart David Davis with a cheery handshake at the European Commission in Brussels.
The Brexit Minister, David Davis, started talks with the European Union officials in Brussels to work out a deal on Britain's exit from the European Union and its future relationship with the common currency bloc.
David Davis began negotiations yesterday.
May said the talks had made a "very constructive start". "And I am not the only one", Michel said.
Austrian Chancellor Christian Kern said May's proposals are "a first step" but warned there are still many European citizens in Britain who would not be covered by the proposals.
Whatever happens with interest rates and in the Brexit talks, credit ratings agency DBRS says uncertainty "is likely to adversely impact the economy and the fiscal accounts". We want to make sure that the withdrawal of the United Kingdom happens in an orderly manner.
"In Europe, I never have illusions because I don't want to lose them", Juncker said.
"In the first phase, the negotiation rounds will be broken down into three groups: citizens' rights, the single financial settlement, and other separation issues", Barnier said. "We are now at the start of all this and we don't know whether it will be a sprint or a marathon", he said.