A worker arranges flags at the EU headquarters as Britain and the EU launch Brexit talks in Brussels, June 19, 2017. [Photo/Agencies]

Britain and the European Union have on Monday started formal talks on the UK's departure from the EU, with the British government still wracked by internal disagreement over what kind of deal they want.

UK Secretary of the State for Exiting the European Union David Davis sat down with his team to start the process, with Michel Barnier and his aides.

The system worked out by both sides called for a monthly cycle, consisting of two weeks of officials laying out the month's negotiating points, followed by a week's hard bargaining between Davisand Barnier. The fourth week would then allow both sides to brief their respective governments - 27 in the case of the EU - before moving on to the next agreed agenda item.

The UK government's ruling Conservative Party has been divided over the deal, with long-standing opponents of the EU membership demanding a so-called "hard Brexit". Others, including Chancellor of the Exchequer Philip Hammond, urged a "soft Brexit", which would include remaining in the single customs union, accepting the free movement of EU citizens, and continuing to recognise the Europe Court of Justice.

On Monday, the Guardian reported EU officials were concerned the UK government's current weakened state, plus concerns it was distracted about continuing terror attacks and a major deadly fire at a London residential tower block, could mean a disjointed approach in the exit talks.

Prime Minister Theresa May, who previously had a comfortable 17 seat parliamentary majority, held an unexpected snap general election earlier this month, which left her short of the overall number of seats needed to govern, although her Conservatives were the largest party.

A reminder of the problems faced by May and her colleagues came early on Monday, when a van was driven deliberately into worshippers leaving a north London Mosque, killing one and injuring ten. The driver, a white male, was arrested and charged with murder. Eyewitnesses said he shouted "I want to kill Muslims" as he was detained.