Oh, very interesting, I didn't realise intent was part of it. There's even advice from the CPS (linked from that Wikipedia page) about what to do about someone claiming to just be generally a naturist [1]

[1] https://www.cps.gov.uk/legal-guidance/nudity-public-guidance...

It includes this:

> Nudity in public alone with no aggravating features is very unlikely to amount to [public nuisance] (or any other) offence.