Often no permit, but almost always insurance.
Film London notes that a small crew of five or fewer, shooting with handheld equipment without blocking the way, can usually film on the street without a permit. Data from
FilmFixer shows the same rule of thumb: five people or fewer, handheld or tripod only, and keep 1.5m clear for pedestrians. Step outside that and you'll need permission from the local Borough Film Service, especially for parks, markets, estates or Tube and train stations, which always need sign-off. Either way, public liability insurance of at least £5m is expected, and if cover is new to you, here's what to know about
short-term production insurance.
Pro tip: Booking a private Peerspace venue means you're shooting on private property with the owner's permission, so you sidestep the public-space permit maze of parks and streets, though you should still confirm any insurance the host asks for.