How do you define a "British" film?
Is The Life and Death of Colonel Blimp (1943) a "British" film?
Most people would say so, but it had:
A Hungarian writer [producer & director] (Emeric Pressburger)
An Austrian star (Anton Walbrook)
A Polish composer (Allan Gray)
A French cinematographer (Georges P√É¬©rinal)
A German designer (Alfred Junge)
and that's just looking at the more important people involved in it.