The EU's chief negotiator Michel Barnier welcomed Britain's Brexit minister David Davis in the European Commission, where working groups commenced detailed discussions on citizens' rights, financial settlement, and other issues, such as jurisdiction of the EU's top court and the UK's Northern Irish border with Ireland.
He will come back to Brussels on Thursday for more talks with Barnier and a news conference.
More than a year after the Brexit referendum, some still argue that it would be in Britain's interests to remain in the European Union, and retain the benefits of free movement of people, capital, goods and services.
That worries European Union negotiators who stress that 20 months until Brexit is very little time to negotiate an orderly departure.
Over the weekend British newspapers were full of reports of a civil war within her cabinet, with finance minister Philip Hammond, in particular, being targeted over allegations he was trying to derail Brexit.
Barnier, a former French cabinet minister who was flanked at the table by his German deputy Sabine Weyand and French strategy chief Stephanie Riso, has urged the British to give more detail on what they want, more than a year after they voted for Brexit.
Video Davis Let's get down to business
Sterling snapped a three-day advance ahead of the talks that are likely to focus on protecting citizens' rights, which has been a key sticking point so far.
Even though May had insisted that the Brexit process can't be reversed, her government will not be able to pursue the firm Brexit line she favored, following an undesired result of the June snap election, in which her party lost majority in the House of Commons.
Common ground was very much lacking last week after British foreign minister Boris Johnson's remarked that the European Union could "go whistle" over its massive Brexit bill demand, drawing a rebuke from Barnier.
United Kingdom finance minister Philip Hammond said Sunday that Britain will take responsibility for the money it owes, but dismissed the 100 billion euro figure as "ridiculous". "But a Labour Brexit would look very different to the race-to-the-bottom tax haven backed by this Conservative government", he said. Earlier in March, British Prime Minister Theresa May had set a two-year timetable for leaving the EU.
"David Davis has vowed to "get down to business" and hit the "substance" of Brexit talks as a new round kicks off today", wrote the Daily Mirror.
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News of the revision comes as Republicans delay their summer recess by two weeks to mid-August, the news service writes . The Senate quickly approved a revised version of the bill, but House Democrats objected to having their power curtailed.