The European Union's chief negotiator Michel Barnier is concerned at the slow progress of Brexit talks, while his British counterpart David Davis is calling for "imagination and flexibility" to move on.

British officials arrived in Brussels on Monday hoping to push the EU towards talks about their post-Brexit ties, which the bloc refuses to launch until there is agreement on London's exit bill and other pressing "divorce" matters, including the rights of EU citizens in Britain after March 2019.

"To be honest, I am concerned. Time passes quickly," Barnier told reporters as he welcomed Davis back for a new round of talks. The third formal session since the process began in June, it is due to wind up on Thursday.

"We must start negotiating seriously," Barnier said. "The sooner we remove the ambiguity, the sooner we will be in a position to discuss the future relationship."

He welcomed a series of proposals London made over the summer break, but made clear they fell short of what EU leaders want to see before they negotiate a free trade agreement the British government wants.

Impatient with the structure of talks agreed among the 27 other states and now binding Barnier's negotiators, the British position papers made frequent reference to a future relationship with the EU rather than just the immediate task of bringing legal clarity for people and business when Britain leaves.

"We want to lock in the points where we agree, unpick the areas where we disagree and make further progress on the whole range of issues," Davis said.

To do that would require "flexibility and imagination from both sides", he said.

The EU and Britain seem far apart on agreeing how much London should pay the bloc on departure to account for previous commitments.