A beaming Brexit Secretary David Davis, a veteran campaigner against European Union membership, told a sombre Michel Barnier, the EU's chief negotiator, that his team aimed to maintain a "positive and constructive tone" during "challenging" talks ahead in the hope of reaching a deal that was in the interests of both sides.
"The most important thing I think now is for us to look to the horizon, think about the future, and think about the new partnership, the deep and special partnership that we want to build with our friends".
Ushering Mr Davis into the European Commission's Berlaymont headquarters, Mr Barnier said that he wanted to able to report to a summit of EU leaders on Thursday that Britain had dropped its opposition to a "sequenced" timetable of talks.
This breaking news story is being updated as more information emerges - please refresh the page for the most recent version.
The Brexit secretary's comments come as formal negotiations between the United Kingdom and the European Union are set to commence, and shortly after European Union leaders such as French president Emmanuel Macron have attempted to encourage Remain campaign diehards by saying "the door is always open" to staying.
Officials on both sides play down expectations for what can be achieved in one day.
Britain already appears to have capitulated to the EU's insistence that talks first focus on three key divorce issues, before moving onto the future EU-UK relationship and a possible trade deal. With or without a deal, Britain will be out of the European Union on March 30, 2019.
A spokesman for the Department for Exiting the European Union said: "We believe that the withdrawal process can not be concluded without the future relationship also being taken into account".
One EU negotiatior said that a weak Tory government "increases the risk" of no deal being done and that "we do not want to be the ones making the situation more difficult".
Mr Davis's agreement to Monday's agenda led some European Union officials to believe that Ms May's government may at last coming around to Brussels' view of how negotiations should be run.
May had promised to take Britain completely out of the bloc's common trading area and slash the number of people coming from the EU. Officials on both sides have until March 2019 to work out a deal, after which Britain will official exit the EU.
With a further million British expatriates in the EU, May too wants a deal on citizens' rights, though the two sides are some way apart.
The so-called Brexit bill is likely to be the biggest hurdle in the early negotiations. The EU insists that should wait until an outline agreement on divorce terms, ideally by the end of this year.
While French President Emmanuel Macron and German Finance Minister Wolfgang Schaeuble last week said the United Kingdom would be welcomed back if it made a decision to reverse Brexit, polls suggest little momentum behind a rethink.
The euro got an overnight boost after French President Emmanuel Macron secured a comfortable majority in parliament in Sunday's election.