Foreign Secretary Boris Johnson has been accused of offering British people a vision of life outside the European Union that is "intellectually impossible" and "politically unavailable".
Dutch finance minister Jeroen Dijsselbloem warned the UK could not expect continued unfettered access to European markets after Brexit unless it accepted free movement of labour.
He said that both the UK and the EU would be worse off as a result of the referendum vote to leave, and he accused Mr Johnson presenting arguments about Britain's future prospects that were "intellectually impossible".
His comments came after Mr Johnson suggested that the UK still wanted a "dynamic trade relationship" with the European Union although it would "probably" have to leave the EU customs union.
"We probably will have to come out of the customs union, but that's a question I am sure will be discussed," he told the Czech daily Hospodarske noviny in comments translated by the Politico Europe website.
Downing Street was quick to play down the remarks, insisting that no decisions had been made, while Mr Dijsselbloem said the Foreign Secretary's comments did not make sense.
"I think he is offering to the British people options that are really not available. To say 'we could be inside the internal market, keep full access to the internal market, but be outside the customs union' - this is just impossible, it doesn't exist," he told BBC2's Newsnight.
"The opposite does exist. We have a customs union with Turkey but Turkey is not part of the internal market. So he is saying things that are intellectually impossible, politically unavailable, so I think he is not offering the fair approach that gives the British people a fair view of what is ahead."
The customs union allows the movement of goods among those countries who are members, but members also have to apply the same tariffs to goods that imported from outside which is seen as a disadvantage by some Brexit supporters who want the UK to be able to negotiate its own deals.
Mr Dijsselbloem warned that whatever the outcome of the Brexit negotiations, the economies of the UK and the EU would both suffer.
He said: "There is no win-win situation. It is going to be a lose-lose situation.
"In the best case - if we set aside all emotions and try to work out an agreement which is least damaging to the both of us - we can minimise the damages for the UK economy and for the European economy.
"Britain and British companies and international companies in the UK have full access to the European markets without any hindrance or customs duties, etc. So some of that will disappear. But it is going to be a step back.
"The UK will be outside the internal market and there will be some hindrances. The full free movement within the internal market can only be available if the UK also accepts the other freedoms of Europe, including migration within Europe."
Earlier however, German chancellor Angela Merkel appeared to suggest that there could be some room for manoeuvre over free movement of labour - which Theresa May has made clear Britain will curb once it is outside the EU.
In comments quoted by The Daily Telegraph, the EU's key power broker warned that making an "exception" for Britain would "endanger" the principles of the EU.
However, when it came to the finer details of how freedom of movement was applied she indicated that there was scope for discussion.
"I personally am of the view that we will have to discuss further with the (European) Commission when this freedom of movement applies from," she said.
While offering "fair" negotiations to the UK, Mrs Merkel added: "First, however, Britain must explain in what manner it would like this exit."