The European Union and Britain have little less than two years to decide the terms before the divorce. British PM Theresa May's cabinet appears bitterly divided over the type of outcome it wants from the talks.
British and European Union envoys on Monday began the first round of negotiations on Britain's divorce from the EU.
Both sides had said it was high time to tackle details, though feuding within the London cabinet over Brexit terms may trouble the process.
EU leaders want British Prime Minister Theresa May to rally her polarised nation – and her fractious cabinet – swiftly behind a clear, detailed Brexit plan. There is a little less than two years to decide the terms before Britain leaves, deal or no deal, on March 30, 2019.
EU leaders are keen to minimise economic and social disruption across Europe as its second-biggest economy cuts loose from the continent after four decades being a member.
Chief EU negotiator Michel Barnier will press UK Brexit Secretary David Davis to agree to Britain covering substantial, existing British financial commitments and offer more detail on Britain's approach, clouded by infighting within May's cabinet.
"We made a good start last month but ... we are now getting into the substance of the matter," Davis told reporters as he was welcomed at the European Commission in Brussels by Barnier, a little more than a year after Britons voted by a narrow majority to leave the EU.
Davis and Barnier shook hands for the cameras at the European Commission's Berlaymont headquarters before a first full session of a scheduled four days of talks.
"We will now delve into the heart of the matter. We need to examine and compare our respective positions in order to make good progress," Barnier told reporters.
Davis said it was "incredibly important" to make 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 reinforce them".
"Now it's time to get down to work and make this a successful negotiation," he said before Davis and Barnier headed off for talks.
Both men declined to comment further, with Barnier saying they would brief the media on Thursday after their teams have spent four days tackling a range of priority issues.
After a June snap election in which May's Conservatives lost their majority, her cabinet appears bitterly divided over the type of outcome it wants from the Brexit talks. Finance minister Philip Hammond has emerged as the champion of a "soft Brexit" prioritising trade ties with the EU over curbing immigration.
He said he came under attack at the weekend from hardline Brexiteers "who are not happy with [my] agenda" after a series of cabinet leaks intended to undermine him.
But he suggested his view that Britain would require a gradual transition towards Brexit aimed at limiting the damage for business and jobs was now gaining traction in May's government.
EU and British citizens' rights, the financial settlement and the issue of the UK's border with Ireland are on the top agenda for the talks. It has been dominating headlines across Europe.
Funny side of Brexit
While Brexit has split opinions which threatens to create new tensions, it has also provided raw material for newspaper cartoonists across the EU, giving readers some much needed light relief.
TRT World 's Simon McGregor-Wood reports from London.