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The EU's Brexit chief has savaged Britain's "impossible" demands and warned "time is flying" in a nightmare end to four days of talks.

Michel Barnier accused top Tory David Davis of failing to honour his obligations over Britain's divorce bill as the pair clashed in an ice-cold press conference in Brussels.

Brexit Secretary Mr Davis insisted he was being "pragmatic" and there had been "concrete progress" on several issues in the third round of talks on leaving the EU.

He said: "The UK’s approach is substantially more flexible and pragmatic than the EU. We urge the EU to be more imaginative."

Bur Mr Barnier took a dramatically different tone - accusing Britain of "nostalgia" and warning there had not been "sufficient progress" to let EU leaders open the crucial next stage of talks, on Britain's future relationship, in October.

Mr Barnier - who was forced to deny being "angry" - blasted British officials for spending three hours taking apart the EU's plan for a divorce bill line-by-line yesterday.

"EU taxpayers should not pay as 27 for obligations undertaken as 28. It would not be fair," he said bluntly.

(Image: REX/Shutterstock) (Image: REUTERS)

"In July, the UK recognised that it has (financial) obligations beyond the Brexit date.

"But this week the UK explained its obligations will be limited to their last payment to the EU budget before departure."

Mr Barnier said the EU already had long-term loans to Ukraine and European Development Fund investment around the world.

"It’s clear the UK does not feel legally obliged to honour these obligations after departure," he fumed.

British Cabinet minister Mr Davis insisted his approach to the divorce bill was right.

"We have a duty to our taxpayers to interrogate it rigorously," he said.

"At this round we presented our legal analysis.... It’s fair to say across the piece we have a very different legal stance.

(Image: REX/Shutterstock) (Image: REX/Shutterstock)

"The settlement should be in accordance with law and in the spirit of the UK’s continuing partnership with the EU."

Mr Barnier said there had been "useful clarification on a number of points," such as border workers and the future of the border with Northern Ireland.

But he warned: "We did not get any decisive progress on any of the principle subjects."

Meanwhile Mr Barnier said Britain's recent position papers setting out a planned relationship with the EU single market and customs union were "simply impossible".

"You cannot be outside the single market and shape its legal order," he said.

"The single market's capacity to regulate, to supervise, to enforce our laws must not and will not be undermined by Brexit."

(Image: REUTERS) (Image: AFP)

(Image: AFP)

Barnier made clear the EU's and Britain's positions on Brexit remained so far apart there was little chance the EU would agree to start talks about its future relationship with London as had originally been expected in October.

"Which such uncertainty - how can we build trust and discuss future relationship?" Barnier said.

"We are quite far from being able to say that sufficient progress has taken place, sufficient for me to be able to recommend to the European Council that it engage in discussions on the future relationship between the UK and EU."

The visit came as Tony Blair descended on Brussels to meet European Commission President Jean-Claude Juncker - kissing him on the cheek.

(Image: AFP)

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Mr Davis declined to comment on the movements of the ex-PM, who's vowed to sabotage Brexit, because he is a "private citizen".

On the Brexit talks he added: "It's only through flexibility and imagination that we will achieve a deal that works truly for both sides.

"In some areas we have found this from the Commission's side, which I welcome, but there remains some way to go."

It came after a fractious four days that saw vicious briefings and counter-briefings to newspapers from each side.

Reports claimed UK officials criticised their EU counterparts describing them as "incapable of being able to carry out the Brexit negotiations".

A source told the Times: "Nobody would write a cheque on the basis of the Commission's four-page paper."

The European Parliament's Brexit chief Guy Verhofstadt warned yesterday that progress was too slow.

He warned it would be "very difficult to say there has been sufficient progress" by the time EU leaders meet in October to start talking about Britain's future relationship.

Mr Barnier himself told Britain to "start negotiating seriously" in an icy start to the talks on Monday.