18 July, 2017
"We're into a real process now with the start of negotiations and I think you'll find the cabinet rallying around a position that maximizes our negotiating leverage and gets the best possible deal for Britain".
High on the list of priorities is the status of European Union citizens in Britain after Brexit, the UK's bill for leaving and the Irish border.
The two hope there will be sufficient progress on those issues this summer so that talks on a future relationship between the two can start in October or November.
Mr Barnier said: "I look forward to our negotiations this week".
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.
Her Brexit minister, veteran anti-EU campaigner David Davis, will meet Barnier, a French former cabinet minister, at the European Commission's Berlaymont headquarters at 9:15 a.m. (0715 GMT) on Monday for a brief public handshake before formal business begins. The European Parliament warned last week it could veto the final deal if Britain doesn't give EU citizens more rights if they choose to stay in Britain after Brexit, which is due to take place in March 2019.More news: Alfred Angelo closes the doors
Prior to his departure, Davis said it was important to now "get into the substance of the matter", and acknowledgement that little was accomplished during the opening of negotiations in June.
The EU has demonstrated increasing confidence in recent weeks, accusing Britain of dithering over whether it wants a "hard" or "soft" Brexit more than a year after the shock referendum that propelled May to power.
Britain's "divorce bill" is estimated at about €60 billion although some commentators have suggested it could be as large as €100 billion.
On Thursday, the British government introduced a draft law that would formally end Britain's European Union membership, as preparation for eventually divorcing the bloc and gaining back legislation power of parliaments.
As Conservative Prime Minister Theresa May tried to silence ministers who have briefed the media on splits in her cabinet what the terms for Britain's divorce from the European Union should be, newspaper critics on the left let rip.
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.