After an initial meeting last month where the structure of the talks was determined, Britain's Brexit minister, David Davis, met up with the EU's chief Brexit negotiator in Brussels ahead of four-days of discussions.
Barnier said on Monday that the talks, which run to Thursday, would "delve into the heart of the matter". "We need to examine and compare our respective positions in order to make good progress".
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. "It's a mess. Nobody would want to see them like this", said one European diplomat handling Brexit.
But one unnamed Cabinet minister was reported have hit back, claiming Mr Hammond was part of an attempt by "the Establishment" to prevent Britain ever leaving the EU.
But in London there was fresh turmoil as weakened Prime Minister Theresa May prepared to urge her warring ministers to end damaging leaks against each other over Brexit.
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These talks focus on Britain's arrangements to leave the EU.
Davis has warned May repeatedly that the uncertain fate of the citizens was souring his meetings with member-states, two people familiar with the matter told Bloomberg this month.
But this next round of talks is unlikely to be definitive: European Union officials expect to map out their differences with the British rather than strike any final agreements.
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. In particular, the delegations are expected to focus on how to manage new border arrangements, what rights EU and United Kingdom citizens will hold post-Brexit and, most controversially, how much London owes the Union. "This government is facing a ticking clock over the Brexit negotiations", Hammond said on Sunday.
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 European Union citizens in our country".