The leaders are also likely to shape more clarity on the UK-EU relationship post the exit and the nature of trade deals between them. The last round, according to the current schedule, will start on 9 October, 10 days before the European Union summit where leaders are expected to assess the progress made. Davis said she will tell them about plans to guarantee rights for some 3 million European Union citizens in Britain under a proposal to be made next week.
Davis said the talks were off to a "promising start" and denied that Britain had caved in on the sequencing of the talks. Both say they want a reciprocal agreement although the Europeans say the British side does not appear to appreciate just what that involves. "That will be in our mutual interest, but we 27 will formulate our interests very clearly and hopefully together".
David denied any retreat by his government, noting that "both sets of dialogue will continue once the European Union 27 will agree that divorce talks have reached "sufficient progress".
"We will then publish a detailed paper outlining our offer on (next) Monday which I believe will form the right basis on which to reach agreement", he said.
Only when "sufficient, concrete progress" on the first phase has been made will Mr Barnier recommend to the European Council that the negotiations can enter the next stage, taking in the future trading relationship, with that recommendation possibly coming at October's summit of EU leaders.
It announced in a separate statement that Parliament would sit for two years instead of the usual one to give MPs enough time to fully consider the laws required to make Britain ready for Brexit.More news: Real Madrid boss Perez tackles Ronaldo problem
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"There is more that unites us than divides us", Davis said, referring to the latest reported terror attack overnight in London and the loss of lives in forest fires in Portugal.
The association represents 3,200 businesses with a million employees in Germany making industrial machinery.
As Brexit negotiations begin, five of Britain's business groups have petitioned the government to reach a deal giving the United Kingdom continued access to the single market and customs union in the interim.
European stocks rose on Monday, partly on optimism about the talks actually getting underway after months of sniping and uncertainty, analysts said.
"It is the United Kingdom that's leaving the European Union, not the other way around", Barnier said sharply, speaking of "unravelling" 44 years of relations. Led by Germany, Brussels had insisted from the beginning that Britain's decision past year to leave Europe clearly meant it was leaving Europe, with all the attendant privileges. We keep hearing that they don't want a 'Norway model, ' they don't want a 'Swiss model, ' they want to leave the customs union, the internal market, they want to limit migration. Finally he claimed the negotiations would offer "a revolution" which would solve a longstanding issue in British politics.
Mr Johnson, who has previously described the estimates emerging from Brussels of the so-called "divorce bill" as "absurd", added: "I think the whole thing, the whole process will lead to a happy resolution that I think can be done with profit and with honour for both side and that's what we're aiming for".