British cities should introduce a “hotel tax” on tourists to keep museums and galleries open for free, the director of the Victoria and Albert Museum has argued.

Tristram Hunt, who joined the museum last year, said he would be “very much in favour” of levying a charge on overseas visitors at hotels, which would be used to support local culture.

Suggesting it was unfair that British art-lovers must pay a tourist tax in major cities such as New York and Rome before also buying expensive tickets to enter their galleries, he said implementing a similar system could help struggling local museums that had been “absolutely smashed” by finding cuts.

Speaking at the Royal Academy’s Festival of Ideas on Saturday, Hunt admitted he had previously got it wrong when he suggested, when a Labour MP in 2011, that it was time to reintroduce charges for the national museums.

The debate around maintaining free entry for museums and galleries has been under discussion for decades, with all government-supported arts institutions becoming free in 2001 in an attempt to widen access for all.