In a press conference following talks with UK Brexit Secretary Dominic Raab, Mr Barnier said the EU had “doubts” that the UK’s plan for a ‘facilitated customs arrangement’ where London would collect tariffs and perform checks on goods destined for Europe could work.
The two men pledged to meet every week ahead of a crucial EU summit in October, when both sides hope the UK’s withdrawal agreement can be signed off by European leaders.
Mr Barnier said that he wanted to "bring new energy into these negotiations" over the coming weeks, and said UK proposals on foreign policy and security marked "a real step forward".
But he said: "In contrast, on our future economic relationship, it comes as no surprise that finding common ground between the EU27 and the UK is more difficult."
Mr Barnier warned that retaining control of the EU's money , law and borders also applied to the EU's customs policy.
"The EU cannot and the EU will not delegate the application of its customs policy and and rules and VAT and excises duty collection to a non-member who would not be subject to the EU's governance structures."
And he said the ‘backstop’ plan to ensure there was no hard border in Ireland had to be resolved before any withdrawal agreement is signed off.
The UK has said it cannot accept a backstop that effectively keeps Northern Ireland alone in the EU customs union, erecting a trade frontier in the Irish Sea.
Mr Barnier said he had “no objection in principle” to a backstop being applied to the whole UK, but added: “We have doubts that it can be done without putting at risk the integrity of our customs union or commercial policy our regulatory policy."
Mr Raab was challenged over his claim this week that the UK may refuse to pay its £39 billion ‘divorce bill’ if a deal isn’t reached on future trade. In Brussels, he said: "We have been clear, as the EU is, that there is no deal until we do the whole deal.
"The various different aspects - the Withdrawal Agreement, the protocol [on the Irish border] and the political declaration [on future relations] - come as a package as a whole.
But Mr Barnier insisted that the commitment on the financial settlement made by Mrs May last December was regarded by Europe as final.
He told Mr Raab: "It is quite right that there is agreement on nothing until we have agreement on everything.
"But what is perfectly clear to the 27 EU member states and the European Parliament is that what has been agreed in December and March has been agreed for good."