David Davis and Michel Barnier leave after addressing journalists in Brussels | Emmanuel Dunand/AFP via Getty Images After 3 rounds of Brexit talks, a gaping divide EU chief negotiator Michel Barnier insists leaving the EU and the single market will have consequences for the UK.

Brussels had long warned the U.K. that Brexit could not mean keeping the privileges of EU membership without the obligations.

But after three rounds of formal negotiations, and a flurry of papers laying out where it stands on key issues, London's approach looks less to EU leaders like the "cherry-picking" they warned against and more like a demand for a whole cherry pie — with a big scoop of ice cream on top to boot.

On every major issue, from rejecting the EU's approach to a financial settlement to trying to fast-forward the discussion of a new trade and customs deal, and refusing to accept the jurisdiction of the European Court of Justice, the U.K. has laid out a vision of a post-EU future in which things only get better for Britain — and at no cost.

These disagreements are at the heart of an impasse that both sides fear no amount of negotiating will break: EU leaders and their negotiators insist that Britain must accept that there are negative consequences of leaving the EU while the U.K. government is intent on proving to its constituents that the country is better off single than attached.

"I see in several [of the U.K.'s] proposals a certain nostalgia, through precise demands, which would amount to wanting to continue to benefit from the advantages of the EU's single market without being part of it," the EU's chief negotiator, Michel Barnier, said at a joint news conference Thursday to wrap up the latest, abbreviated round of talks, which lasted just two days.

“I wouldn’t confuse a belief in the free market for nostalgia" — David Davis

"Brexit means Brexit," Barnier continued, turning U.K. Prime Minister Theresa May's famous phrase against her. "Leaving the single market means leaving the single market and, if that is the decision, it has consequences."

Barnier's remarks prompted his British counterpart, David Davis, to fire back: "I wouldn't confuse a belief in the free market for nostalgia."

But that shot seemed to fall flat, as Davis was forced to concede that negotiators have made excruciatingly meager progress on the big issues, and that the clock is ticking fast toward the March 29, 2019 deadline — at which point the U.K. will automatically cease to be a member of the bloc, even if no withdrawal agreement has been reached.

Davis also publicly declared a frustration that U.K. officials have voiced privately for weeks — their view that the EU27 are being overly rigid in their demands and have given Barnier and his team no flexibility to compromise. Again repeating his line that the EU's rigid sequencing of the talks (divorce first, future relationship second) makes no sense, Davis implored his interlocutor to put "people over process."

'High-stress week'

While the sides had agreed to hold one week of formal negotiations per month, this week's round was reduced to barely 48 hours, beginning Tuesday at 11:30 a.m. and ending Thursday before noon. Each side described the compressed talks this week as extremely tense — "a high-stress week," Davis said — largely because the U.K. rejected the core basis of the EU's demand for a financial settlement. That position left Barnier and other EU negotiators deeply frustrated.

Brussels repeatedly has sought to portray the financial settlement as a matter of the U.K. fulfilling prior commitments, including its share of the EU's current long-term budget plan, which runs up to 2020 and which the U.K. approved.

At Thursday's news conference, however, Davis characterized the EU position as a "claim" and said the U.K. disputed the legal basis that Brussels had put forward.

"The European Union made a claim on the United Kingdom, on the United Kingdom taxpayer, for a large sum of money —unspecified, but undoubtedly large — and on the basis of what it determined to be our legal obligations," he said.

At another point, Davis said the U.K. had a duty to rigorously "interrogate" the EU position adding: "It’s fair to say, across the piece we have a very different legal stance."

A senior EU official briefed on the talks by Barnier agreed: "On the big things, it will clearly need a different momentum to get somewhere."

That the two sides remain so bitterly divided on the issues that the EU identified as the core divorce terms makes it increasingly unlikely that the European Council at its summit on October 19-20 will determine that "sufficient progress" has been made to move on to the next phase of talks, including a future trade relationship and potential transition period.

The two sides did report technical progress on some points, particularly in relation to preserving the Common Travel Area between the Republic of Ireland and the U.K., as well as on the issues of cross-border workers, social security rights, and ongoing cases before the European Court of Justice.

“We haven’t noted any decisive progress on the principal subjects" — Michel Barnier

But those technical steps forward were far overshadowed by the broader stalemate.

Barnier, who seemed irritated throughout the press conference (although he told journalists he was "calm like a mountaineer"), offered a dark assessment of this week's talks and of where the negotiations seem to be headed. "We haven’t noted any decisive progress on the principal subjects,” he said, adding: "At the current state of progress, we are far from assessing that progress has been sufficiently made to be able to recommend to the European Council that it engage in discussions on the future relationship.”

Davis cast this week's talks more positively, calling them "a productive, important stepping stone." But he also accused the EU of being overly rigid in its approach. That charge is certain to infuriate the EU27 leaders, who view their position as consistent and transparent, even as a large segment of the political and chattering classes in the U.K. seem stuck in the same Leave-Remain debate that raged before the June 2016 referendum.

"Our discussions this week have exposed yet again, that the U.K.’s approach is substantially more flexible and pragmatic than that of the EU because it avoids unnecessary disruption for businesses and consumers," Davis said. "We proposed pragmatic solutions to prevent this disruption and we urge the EU to be more imaginative and flexible in their approach to withdrawal."

Quentin Ariés, Giulia Paravicini and Maïa de La Baume contributed reporting.