Those were, he said, the rights of expatriate citizens and problems of a new EU-UK border, notably cutting across Ireland.
Mr McDonnell told Sky News' Sophy Ridge on Sunday programme: "I am afraid the problem with the Brexit talks is that we have a government in disarray".
And Hammond described the divorce bill figures being bandied around in Brussels as "the most egregious pre-negotiation posturing".
At a press conference held before negotiations begin, Davis said "we are starting this negotiation in a positive and constructive tone". There is more that unites us than divides us.
Mr Hammond was outspoken in interviews yesterday, saying that leaving without a Brexit deal - which the Prime Minister was prepared to do - would be "very, very bad" for the country.
But the situation is very different from 12 months ago when the Brexiteers were riding high, with Prime Minister Theresa May's entire approach called into question after a disastrous election performance on 8 June.
Hammond said Brexit means that Britain will leave the EU's single market and the bloc's customs union, but that he wanted an exit that would support jobs and investment.
Other issues on the agenda, at least in the near term, include establishing residential rights of more than 3 million European Union citizens now living in the United Kingdom - and the 1 million British expats living in European Union member states - once the formal exit is complete.
Brexit department mandarin Olly Robbins and the UK's ambassador to the EU, Sir Tim Barrow, will join Mr Davis for the lunch session.
Macron, a committed pro-EU leader and ally of German Chancellor Angela Merkel, easily won French legislative elections on Sunday, cementing his power base.
While the European Union negotiating team led by Michel Barnier has been ready for months, Britain stalled even after it triggered the two-year process on March 29.
The party has refused to give a time frame for reaching a deal, though May is due in Brussels for an European Union summit on June 22-23 when she will want to show she has a solid grip on power.
Scottish Conservative leader Ruth Davidson, who is newly influential after winning 13 seats in Scotland, has said Britain should prioritise "freedom to trade and our economic growth". She squandered her parliamentary majority in a mistimed election and faces increased domestic pressures following last week's London tower block inferno.
"It's a statement of common sense that if we are going to radically change the way we work together, we need to get there via a slope, not a cliff edge", he said.
In an opening statement that contrasted with Theresa May's bellicose threats to leave with no deal, he hinted that the United Kingdom was prepared to make compromises in some areas.