Arriving in Brussels, Brexit Secretary David Davis said: “Now it’s time to get down to work and make this a successful negotiation.”
He said negotiators had made a good start last month but that they would now be working “on the substance of the matter”.
Despite the round of talks lasting four days, Mr Davis is understood to have returned to the UK after a few hours in Brussels.
His visit included a meeting with Michel Barnier, the European Commission’s chief negotiator.
But a picture of Mr Davis sitting opposite Mr Barnier has caused a bit of a stir – with the Brexit Secretary having no notes or papers in front of him while Mr Barnier has a thick folder of papers.
Mr Barnier earlier offered Mr Davis a “warm welcome” and said the latest round of discussions would “delve into the heart of the matter”.
Also on the agenda this week are the contentious issues of the financial settlement for the UK leaving the EU and the arrangements for the border between Northern Ireland and the Irish Republic.
Mr Davis, whose allies claim 30 Tory MPs are ready to back him if he runs for the leadership, has said his priority for this week’s talks is citizens’ rights, with a new push to lift uncertainty for the three million EU citizens living in the UK and one million Britons living in the EU.
“We made a good start last month, and this week we’ll be getting into the real substance,” he said.
“Protecting the rights of all our citizens is the priority for me going into this round and I’m clear that it’s something we must make real progress on.”
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.”
Meanwhile, there are reports Chancellor Philip Hammond has been accused of Brexit treachery and trying to frustrate the UK’s withdrawal from the EU.
Brexit hardliners in the Cabinet and on the Tory backbenches are furious with Mr Hammond for championing a two-year transition deal to cushion the impact of leaving the EU.
An unnamed senior Cabinet minister is quoted in The Daily Telegraph saying: “What’s really going on is that the Establishment, the Treasury, is trying to f*** it up. They want to frustrate Brexit.”
According to the Telegraph’s source, Mr Hammond sees Brexit-supporters as “pirates” who have “taken the Establishment prisoner” and he is “trying to break out” and get his own way.
The latest reported attack on Mr Hammond from senior colleagues comes after he reacted angrily to a Sunday Times report claiming he told the Cabinet that public sector workers were overpaid.
But in the same interview, the Chancellor – seen as an advocate of a so-called “soft Brexit” – infuriated hardline Tory Brexiteers who want a clean break from the EU by suggesting a transitional period could last two years.