Traders were cautious as four days of Brexit negotiations began in Brussels.
The EU also wants London to accept a bill to cover its share of EU spending commitments made while Britain was a member.
Britain and the European Union (EU) launch a new round of Brexit negotiations here on Monday as conflicting views on "divorce" terms cast shadow on the resumption of talks and a feasible deal seems rather hard to reach for now.
While the EU Commission negotiators each sat with a stack of briefing papers in front of them, the United Kingdom delegation had none, leading to speculation on Twitter as to whether they had actually brought any.
While Mr Barnier will hold a press conference at the close of talks on Thursday, Mr Davis' team has yet to confirm whether the minister will join him.
"We'll now delve into the heart of the matter", Barnier told reporters, saying the two sides need to examine and compare their respective positions.
"For us it is incredibly important that we now make good progress, that we negotiate through this and identify the differences so that we can deal with them and identify the similarities so we can reinforce them", Davis said.
May herself was set to call them to order on Tuesday, her spokesman said. And I would think that, come the month of September/October, we will be able to come jointly to the rest of the (WTO) membership", the European Union source said, speaking on condition of anonymity.The joint approach would address aspects of the EU's WTO membership terms, known as its WTO "schedules", that are not easily split between Britain and the other 27 European Union members: "agricultural tariff quotas, agricultural subsidies and commitments on services trade.
Earlier estimates put the bill between €60 billion and €100 billion.
The first objective is to show enough progress on a divorce package so that the European Union will agree to open talks on a future free trade deal.
Finance minister Philip Hammond, who like May campaigned previous year to keep Britain in the European Union, accused unnamed colleagues of trying to undermine what is seen as his push for a "soft Brexit" that prioritises trade rather than hardliners' demands for controls on European Union immigration or an end to European Union legal oversight.
Her Brexit minister, veteran anti-EU campaigner David Davis, will meet Barnier, a French former cabinet minister, at the European Commission's Berlaymont headquarters at 9:15 a.m. (0715 GMT) on Monday for a brief public handshake before formal business begins.
May's minority government remains fragile one month after the snap June 8 election in which her Conservative Party lost its majority, forcing it to seek an alliance with Northern Ireland's small ultra-conservative Democratic Unionist Party.
Hammond, one of Johnson's main cabinet rivals, said Sunday that Britain will take responsibility for the money it owes, but dismissed the 100-billion-euro figure as "ridiculous". The tensions have shaken the British government, which on Thursday introduced the draft law that would formally put an end to Britain's membership of the EU May faces a battle over the bill, which opponents said included a unsafe "power grab" by London at the expense of Scotland and Wales.
"I think on many fronts it would be helpful if my colleagues - all of us - focused on the job in hand".