Both EU negotiator Michel Barnier and his British counterpart David Davis said after the first negotiating session they were confident of quick progress but said major challenges lay ahead to meet the deadline of March 2019 for Britain to officially leave the bloc.
The 68-year-old Conservative MP for Haltemprice and Howden will be leading the talks on what Britain wants from negotiations, working closely with Parliament to ensure the leave process happens in the two-year negotiation period. "That will be in our mutual interest, but we 27 will formulate our interests very clearly and hopefully together".
But Monday's talks will seek mainly to tie down the timing, with the European Union suggesting monthly cycles over the summer. The European Commission calculates the divorce bill will be nearly €100bn (£88bn), although the net figure will likely be closer to €60bn (£53bn).
Monday's talks however are likely to focus on the practical details of timings for the coming months, with the big, divisive issues left aside for now, officials said. The extent of Britain's exit bill needs to be decided, with the EU27 expected to seek tens of billions of euros they see as London's fair share of programs to which it has committed.
On the face of it, it seems straightforward enough with both the British Government and the European Commission both declaring they want an early reciprocal deal to secure their future rights, marking an amicable start to proceedings.
Many European Union citizens would like to follow Britain in having a chance to vote on membership of the bloc, although fewer than one in five support leaving it.
Brussels insists that those living in Britain now should be able to keep those rights after Brexit. The party has refused to give a time frame for reaching a deal, though May is due in Brussels for an European Union summit on June 22-23 when she will want to show she has a solid grip on power.
"The best way we can spend this week is to rebuild trust", rather than tackle the big hard issues right at the start, another European source said.
Other issues that have to be sorted include the status of the border between Northern Ireland and the Irish Republic.
Is Britain also looking for a free trade deal? While European leaders try to gauge what to expect from Britain, May is so weakened that her own finance minister and the partners on whom she will rely for her majority, Northern Ireland's Democratic Unionist Party, are giving her public guidance.
"Today we are launching negotiations on the orderly withdrawal of the United Kingdom from the EU", said Barnier, a former European commissioner and French foreign minister.
"We're not going to get into - and I know there has been a lot of talk about our position in relation to social issues for example - those are matters for the Northern Ireland assembly".
We'd leave the Customs Union, which means that Britain at the moment is able to export goods to Europe without any tariffs and without any checks at the frontier. Britain's giant banking industry and other business groups see Hammond as their most powerful ally in government and they were anxious when it appeared he might lose his job in the run-up to the election.
An EU-UK trade deal is far from plain sailing, however, with Brussels warning it could take up to seven years after Brexit to agree on one.
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