Fighting for her political survival, May has been trying to strike a deal with a small Northern Irish Protestant party to avoid a second election that could delay Brexit talks and damage the $2.5 trillion economy.
However, it faces the prospect of delivering a Queen’s speech while still thrashing out a deal with Northern Ireland’s Democratic Unionist Party.
May is not expected to announce an agreement with the DUP until next week.
Barnier this week acknowledged “sensitivity” in London at European Union suggestions that Britain might owe it some 60 billion euros in 2019 and said sorting out the issue soon would help a trade deal: “I would like to very quickly play down this question, and find concrete, pragmatic and just solutions”, he said on Monday.
Mr Barnier is due to report back to leaders of the 27 other EU states on Thursday to review progress ahead of a two-day summit of the European Council attended by Theresa May which starts later that day.
“Our focus over the last couple of days has obviously been on the tragic fire a Grenfell Tower in West London and our thoughts are with the families of those who died and the community in that area”, he said.
May wants to negotiate the divorce and the future trading relationship with the European Union before Britain leaves in March 2019, followed by what she calls a phased implementation process to give business time to prepare for the impact of the divorce.
The Chancellor declined to comment on whether he supported Britain’s continued membership of the EU single market or customs union.
“I’m not going to give a blow by blow account of how we propose to take that discussion forward”, he said.
The UK Government wants the talks to take place in parallel during the Brexit process but both sides have made finding a solution to the issue of citizens’ rights a priority.
European Union leaders have given chief Brussels negotiator Michel Barnier no authority to so much as talk about future trade with Britain until he clinches outline deals on Brussels’ priority issues, including London’s exit bill.