It’s a scene most Londoners know well: a normally peaceful, typically photogenic corner of their city has suddenly, unexpectedly become a film set.

Large vans and other utilitarian vehicles are parked haphazardly around the nearby streets, which are also crowded with bulky equipment and cameras, noisy electricity generators, and often, horse-drawn carriages or period automobiles. Groups of people stand and mill about, some in costume, others wearing orange vests emblazoned with words like “security” across them...