"The best way we can spend this week is to rebuild trust", rather than tackle the big hard issues right at the start, a European source said.
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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.
Anxious by immigration and loss of sovereignty, Britain past year voted to end its decades-old membership of the 28-country bloc - the first state ever to do so - in a shock referendum result. She even threatened to walk away from Europe without paying a hefty divorce bill or striking a new trade deal, under the mantra that "no deal is better than a bad deal". An early election this month, in which Prime Minister Theresa May lost her majority, only added to the problems.
May has clung on to power but has so far failed to conclude an agreement with Northern Ireland's ultra-conservative Democratic Unionist Party that would bolster her ability to govern.
That is ultimately a matter for Mrs May, who must first give herself some breathing space in the House of Commons by coming to an understanding with the ten-strong group of DUP MPs. "A deal that supports growth will allow companies to hire more people, raise living standards and improve lives across the country", it adds.
Economic data is beginning to lend extra weight to the argument for a softer approach to Brexit.
A year after Britons shocked the continent by voting on June 23 to cut loose from their main export market, new debate within Prime Minister Theresa May's cabinet on precisely what kind of trading relationship to pursue has perplexed European Union leaders, who warn time is tight to agree terms before Britain leaves in 2019.
"The question is not whether we are leaving the customs union. That's a statement of legal fact", he told BBC television.
May herself will also have a chance to update the other 27 European Union leaders on her Brexit plans at a summit in Brussels on Thursday.
Davis said the talks were off to a "promising start" and denied that Britain had caved in on the sequencing of the talks.
The BBC has been told by European Union sources that the talks will follow the EU's preferred pattern of exit negotiations first, with the future relations between the two sides - including the free trade deal the United Kingdom is seeking - at a later date.
The negotiations kick off in Brussels on Monday with Britain under pressure for stalling the talks and entering the negotiations without a working parliamentary majority fully in place.
"No deal would be a very, very bad outcome for Britain", Hammond said Sunday.
"We each have to assume our responsibility and the consequences of our decisions", he said at the conclusion of Monday's press conference.
All the confident predictions by senior Tories that Britain would leave the European Union on its own terms, and insist if necessary on a so-called hard Brexit, with calamitous consequences on both sides of the Irish border, have swiftly evaporated.
The mood was "incredibly positive" on the first day of Brexit talks between the two sides and they acknowledged that it was time to move quickly, a British source said.