Barnier made clear on Tuesday that while there must be a first phase that excludes trade discussions, he does hope that four weeks of monthly negotiating sessions can get him to the point where he can ask European Union leaders in October to let him move on and discuss how the two sides can keep commerce open from 2019.
London agreed that "English and French will be used as working language".
In carefully choreographed talks that even saw the two men exchange mountaineering gifts, they agreed to discuss divorce issues before negotiations on a future trade deal can start.
Both sides will put top advisers to work immediately on a border agreement between Ireland and the United Kingdom, aiming to make sure the Irish peace agreement and the common travel area should as unaffected by Britain's European Union departure as possible.
And the letter sent by Prime Minister Theresa May to the European Union triggering Article 50 in March had said: "We believe it is necessary to agree the terms of our future partnership alongside those of our withdrawal from the European Union".
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Secretary of State for Exiting the EU David Davis described the talks as a mission to deliver on the will of the British people following the referendum of a year ago.
"We will nearly certainly need an implementation period, outside the (EU's) customs union itself, but with current customs border arrangements remaining in place, until new long-term arrangements are up and running", he said, in a speech yesterday.
"We have the Lancaster House speech, the two white papers and the article 50 letter, all backed up by a manifesto - and so it's the same as it was before", he said, reiterating that Britain will leave the single market and seek to set up a free trade arrangement with the EU.
Britain is "very conscious of how they will use that time sequence to pressure us, and we'll avoid that at every turn", Davis told ITV on May 14. An increasingly concerned European Union has been pushing London to hurry up, with time running out for a deal and three months already passed since May triggered the two-year Article 50 European Union exit process.
"I will do all I can to put emotion to one side and stick to the facts, the figures, and the legal basis, and work with the United Kingdom to find an agreement in that frame of mind", he concluded.