Brexit Secretary David Davis has said talks on the "substance" of EU withdrawal are now under way as a fresh round of negotiations began in Brussels.
The European Commission's chief negotiator Michel Barnier offered Mr Davis a "warm welcome" as the pair met ahead of intensive talks which he said would "delve into the heart of the matter".
Mr Davis said: "We are now getting into the substance of the matter.
"It's four categories really. The issue of citizens' rights, the issue of finance, the issue of separation issues and, of course, separately, Northern Ireland.
"For us it's incredibly important 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 that we can move forward.
"And now it's time to get down to work and make this a successful negotiation."
Mr Barnier said: "I look forward to our negotiations this week. We'll now delve into the heart of the matter.
"We need to examine and compare our respective positions in order to make good progress.
"As you know, our negotiating groups will work on citizens' rights, on the financial settlement and other separation issues.
"David and I will be in contact throughout the week. Rendezvous to take stock together on Thursday."
The talks are taking place against a backdrop of increasingly bitter and public feuding among UK ministers over the Government's Brexit strategy.
Over the weekend, Chancellor Philip Hammond angrily accused Cabinet rivals of trying to undermine his agenda for a "softer" business-friendly Brexit prioritising jobs and the economy.
One unnamed Cabinet minister was reported to have hit back, claiming Mr Hammond was part of an attempt by "the Establishment" to prevent Britain ever leaving the EU.
The Daily Telegraph quoted the minister as saying: "What's really going on is that the Establishment, the Treasury, is trying to f*** it up. They want to frustrate Brexit."
The rowing will be seen as further evidence of Theresa May's weakness after seeing her Commons majority wiped out in last month's general election.
Transport Secretary Chris Grayling attempted to play down suggestions of Cabinet splits over Brexit and criticised those who have been briefing about its meetings.
"I don't see these great divisions that are suggested to me in the Sunday newspapers and I have to say I think all of this is somewhat overplayed," he told BBC Radio 4's Today programme.
Mr Grayling said the suggestion that there were "profound and fundamental differences" between Cabinet ministers on Brexit were "a bit exaggerated", but admitted: "We're not a group of clones, we have discussions around the Cabinet table and outside Cabinet, we debate issues, we decide what's right and then we get on with it.
"I'm very clear that the Cabinet and the party are united behind Theresa May, united in determination to get the right deal for the country in the Brexit negotiations and to make sure we continue the economic progress we've made."
Foreign Secretary Boris Johnson, who is in Brussels on separate business, said: "A very fair, serious offer has been put on the table by the UK Government about citizenship, the value we place on the 3.2 million EU citizens in our country.
"The, I think, very good offer that we are making to them and the security they can have about their future.
"I hope very much that people will look at the offer in the spirit it deserves."