"There are always difficulties, and risks of a failure", Mr Barnier told French TV.
The "Irish question" of how Britain can balance an open Irish border while pulling Northern Ireland from the customs union and single market increasingly appears to be the one issue which could bring the Brexit process screeching to a halt.
Last month, the European Council said that a future trading relationship between the EU and Britain can only be agreed upon if commitments already made by London with regard to the border are "respected in full". "And we are continuing an intensive work programme to engage on all the scenarios set out in the joint report", the British government spokesman said.
The criticism follows news that Brussels has again rejected the UK's proposals to avoid a hard border in Ireland, with the EU's chief negotiator Michel Barnier saying the United Kingdom wants to "cherrypick" its terms.
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The first was a "customs partnership", where the United Kingdom would collect duties on behalf of the EU for goods destined for the European Union.
Mujtaba Rahman, of the political consultancy Eurasia group, said: "This is the first time in an official meeting the UK's Mansion House proposals have been systematically shot down by the European Union side".
The Daily Telegraph said it had been told the UK's plans for Northern Ireland had been subject to a "systematic and forensic annihilation" in what it said was a "detailed and forensic rebuttal".
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A Russian-made aerial bomb weighing 100 kilograms was found near a train track leading into Berlin's main station in 2013 . The Natural History Museum has been closed while parts of the local University have been cordoned off.
Mrs May had previously set out the UK's customs policy in a speech last month.
The "customs arrangement" would have seen technological and administrative measures ensuring trade with the European Union remaining frictionless.
"The Irish and Brussels in particular - but I think backed, as far as I can see, by Berlin and Paris - have said the only solution to this is the so-called backstop Option C, which is what the Commission put in print and got the toxic reaction both from the DUP and the Prime Minister".
But the EU's destruction of the UK's customs proposals adds to a growing consensus that May will have little choice but to remain in the customs union if she wishes to avoid a hard border in Ireland. That, candidly, from everything I've heard from various places is still viewed as a bit of a fantasy island unicorn model.
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Eric Bledsoe and Jabari Parker scored 17 apiece and Thon Maker had 14 for Milwaukee, which trails the best-of-seven series 2-1. When the third quarter rolled around, the Celtics had already committed 13 turnovers, compared to the Bucks' six.
The blow followed a government defeat in the House of Lords earlier this week, which will force a vote in the House of Commons on whether May should negotiate for customs union membership.