And just over a month ago, Mr Davis said dealing with the issue of how the talks would unfold would be the "row of the summer".
European Union diplomats hope this first meeting, and a Brussels summit on Thursday and Friday where May will encounter - but not negotiate with - fellow European Union leaders, can improve the atmosphere after some spiky exchanges.Before lunching on Belgian asparagus, red mullet and meringue cake, the two exchanged gifts that homed in on a shared love of hiking: Davis received a walking stick from Barnier's native Savoy Alps and Barnier a first edition of a French mountaineer's Himalayan memoir - "Regards vers Annapurna".
May's election debacle has revived feuding over Europe among Conservatives that her predecessor David Cameron hoped to end by calling the referendum and leaves European Union leaders unclear on her plan for a "global Britain" which majority regard as pure folly.
Unite assistant general secretary Tony Burke said: "It's absolutely clear that the EU team, Jean-Claude Juncker [president of the European Commission] and Barnier, have their ducks in a row, and it looks from our point of view that we in the United Kingdom are going to be incredibly weak because of the weakness of government".
"The best start would be to abandon the unsafe idea that we could leave the European Union with no deal at all, which would be the worst possible outcome for jobs and living standards in this country".
Barnier said after welcoming Davis that it was important to tackle uncertainties caused by Brexit.
Brexit negotiations start on Monday, with question marks over Britain's approach after Prime Minister Theresa May lost her parliamentary majority in an election meant to strengthen her hand in the talks.
They exchanged gifts - a walking stick from Barnier's native Alps for Davis, a French mountaineer's memoir in a valuable first edition from the Briton to the Frenchman.
The Brexit talks are taking place now despite the UK's inconclusive general election results, which saw the ruling Conservative party lose seats and the opposition Labour party gaining a dramatic rise in the number of votes.
"Theresa is leading the government and I think the government needs to get on with the job", he said.
He and others have also raised the possibility that Britain could remain in the EU.
U.K. TV giant ITV has said since the Brexit vote that the European Union exit has cast a shadow over TV advertising as it has caused "economic uncertainty".
Responding to Mr Barnier, Mr Davis quoted wartime British prime minister Winston Churchill: "No doubt the road ahead will at times be challenging, but as Churchill once said, a pessimist sees the difficulty in every opportunity".
Roth said that "Brexit is a very, very hard operation" and there's only a bit over a year to negotiate it. For one thing, renewed debate in her cabinet on how far to go with her clean break from the single market and customs union has made it hard to present a coherent set of demands in Brussels.
"The only possibility of a soft Brexit is if the European Union itself fundamentally changes, if the European Union allows member states to reclaim more control over their destiny, which is something I've advocated for many years".
"I am neither optimistic nor pessimistic".
Talks will begin at 0900 GMT with a joint press conference by former French foreign minister and European commissioner Barnier and Davis at around 1630 GMT. "I am certainly a determined optimist".
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