May will join an European Union summit on Thursday and, according to Davis, will set out her plans on the residency issue to the 27 other leaders.
The working language of the negotiations will be English and French, with interpretations provided by the European Commission. Both sides stressed their goodwill but acknowledged the task's huge complexity and tight deadline.
The two sides agreed to hold four further monthly rounds of talks, with the next on July 17, on the key issues of Britain's divorce from the bloc.
The EU has said that before it will start discussing a future trade deal with the United Kingdom, it wants to resolve the biggest uncertainties arising from Brexit, including the future rights of around 3 million EU citizens in the United Kingdom and the arrangements for avoiding a hard border between Northern Ireland and the Republic of Ireland.
But the situation is very different from 12 months ago when the Brexiteers were riding high, with Prime Minister Theresa May's entire approach called into question after a disastrous election performance on June 8.
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Davis said the talks were off to a "promising start" and denied that Britain had caved in on the sequencing of the talks.
Davis described the timetable as a "promising start" to the Brexit process."As you heard Michel said, we had a brief exchange earlier about the distinction between being optimistic and being determined".
Mr Hammond also drew plaudits for stressing the importance of transitional arrangements to avoid a "cliff edge" Brexit, including the maintenance of "frictionless" customs union border arrangements for an "implementation period" after leaving the bloc.
"Before long, we will all begin to find out the extent to which Brexit is a gentle stroll along a smooth path to a land of cake and consumption", Carney said in an address to bankers, which was postponed from last week by a deadly fire in a London tower block.
The latest opinion poll from Survation, of more than 1,000 people between 16 and 17 June, found that 57% of respondents opposed a second European Union referendum, while 38% of people backed another plebiscite. With now only 21 months to sign and ratify the exit deal, there is a limited time for any trade agreement. Crucially, members of the Customs Union can not negotiate their own trade deals elsewhere in the world, as they are tied to the tariff arrangements of the 28-nation bloc.
"We are already hearing protectionist agendas being advanced, disguised as arguments about regulatory competence, financial stability and supervisory oversight", he said.