The V&A in London has said a no-deal Brexit could cost it millions of pounds and limit its ability to stage major exhibitions.
It is one of a number of leading tourist attractions in London to warn that leaving the EU without a deal in place could result in a loss of staff, huge import tax bills and cuts to research grants.
In memos released under Freedom of Information legislation, the V&A said it could be hit with a £25 million import tax bill and a cut in visitor numbers.
A legal note written on September 4 also warned the “worst-case scenario” could even see the museum temporarily close its doors.
V&A director Tristram Hunt, a former Labour MP, told The Evening Standard: “The big one for us is how a no-deal Brexit would affect putting on exhibitions and taking our exhibitions around the world.
“Our ability to hold blockbuster exhibitions while having to pay import duties would be really problematic.
“Our ability to promote British soft power and influence through exhibitions like David Bowie Is and Pink Floyd would be seriously compromised.
“That’s bad for the London visitor economy. Four in five visitors to London come for the culture, and they are drawn by great museums and world class exhibitions. It is also potentially damaging for British influence abroad.”
The Department for Culture, Media and Sport (DCMS) has said they expect a deal to be agreed before the UK leaves the EU.
A DCMS spokesman said: ” Like a range of institutions, museums are taking a responsible approach to the UK’s exit from the European Union, by modelling potential impacts on business operations, including workforce and visitor numbers.
“We are working closely with them to ensure they are fully supported”.
A spokesman for V&A Dundee, which opened in September said: “We don’t have any comment to add on this DCMS planning for Brexit.”
“Our upcoming exhibitions will be announced later this year.”
V&A Dundee’s Scottish Design Galleries feature more than 300 objects from the V&A’s collections in London while its temporary exhibition gallery hosts major touring exhibitions.
Other museums to express concerns about the impact of a no deal Brexit include the Natural History Museum, The Royal Museums Greenwich and National Museums Liverpool.