Austria's chancellor Sebastian Kurz has told Theresa May it is important the UK avoids a hard and disorderly Brexit as the prime minister continued her charm offensive on EU member states.
In a trip to Salzbug, May held talks with both Kurz and the Czech prime minister Andrei Babis to sell the appeal of trading with a post-Brexit Britain.
Barnier said the EU cannot and "will not delegate the application of its customs policy and rules, VAT and excise duty collection to a non-member".
This had been at the heart of May's facilitated customs arrangement, whereby the UK and the EU would collect tariffs on each other's behalf.
Kurz said that while he viewed Brexit "negatively", it was important negotiations between the two sides did not result in a hard Brexit, defined as the UK coming out of the single market and customs union, with a solution on the table by October.
The UK's "rainbow" tour of the continent has seen Foreign Secretary Jeremy Hunt meet his German counterpart in Berlin, while the UK chancellor, home secretary, business secretary and the minister for the Cabinet Office are also meeting counterparts across Europe over the summer.
It comes as the EU's chief negotiator Michel Barnier signalled there were key pillars of May's plan for the UK's future relationship with the EU that he could not accept.
This had been at the heart of May's facilitated customs arrangement, whereby the UK and the EU would collect tariffs on behalf of the other.
Yesterday a YouGov poll revealed that the number of voters supporting a second referendum on the terms of the final Brexit deal had supposed those against for the first time.