Can I shoot a short on tourist visa?
I saw this under the immigration rules: PA.14.3. Film crew (actor, producer, director or technician) employed by an overseas company may visit the UK to take part in a location shoot for a film or programme or other media content that is produced and financed overseas.
The legal answer to this is quite murky. But in practice, if it's just you and a camera shooting scenery in natural light, it's highly unlikely anybody would care, and in the unlikely event that they did, it would difficult to prove that this is "work" as opposed to you recording your holiday.
It's a sliding scale though, and the more "professional" your shoot gets (actors, lighting, staging, other cameras), the more work-like it becomes.
