British negotiators, of whom over 100 were taking part in up to five separate forums at the European Union headquarters, presented their legal assessment of an European Union demand that Juncker has said might leave London paying Brussels some 60 billion euros ($72 billion) - a sum May's ministers have dismissed as unacceptable.
He claims official papers setting out the UK Government's positions were not satisfactory and it was "crystal clear" there is a lot of work to be done before talks on a future trade deal could begin.
Talks on trade will likely be delayed until the winter, as the United Kingdom refuses to admit that it is liable to pay a divorce bill, blocking progress in negotiations.
"The question is to know if we must put an end to the negotiations - which is a purely theoretical question as there are no negotiations".
"And the sooner we remove the ambiguity the sooner we will be in a position to discuss the future relationship and to a transitional period", Barnier said.
"Mr. Verhofstadt's role as Brexit coordinator is to act as a link between the European Parliament and the Commission".
Barnier had demanded on Monday that London start "negotiating seriously" as a March 2019 deadline looms and the talks stall over what comes first - the divorce settlement or Britain's future relationship with the bloc.
Like the Conservatives and much of the country, Labour is split over Brexit, and by offering this kind of proposal has opened the way for different factions to put forward their views of how Britain should leave the EU.
The UK's Davis insists the country wants a mutually beneficial trade deal, but there are points on the European Union agenda that London will never accept - despite calls from the Labour Party to remain in the single market at least. He added, "they have made it quite clear that we can not honor the decision of the referendum if we remain in the customs union and the single market".
The European commission president, Jean-Claude Juncker, repeated this message on Tuesday, when he told an audience of EU diplomats he was disappointed by the British government's approach to the negotiations.
"I did read, with the requisite attention, all the papers produced by Her Majesty's Government and none of those is actually satisfactory", Mr Juncker said yesterday. Two more rounds are scheduled before the October summit.
He stressed: "The EU will not step back one millimetre from its position in defence of the rights of European citizens".