In most cases, no, you don’t need someone’s permission to film them in a public place.
Legally, public spaces come with what’s known as no reasonable expectation of privacy. If someone is walking down the street, sitting in a park, or passing through a public square, they can legally appear in your footage without you needing to ask first.
Where things get more nuanced is how that footage is used.
If you’re filming for personal projects, documentary, news, or editorial purposes, consent isn’t usually required, but many filmmakers still ask [for consent] where practical/possible. Not because they have to, but because it’s good practice and helps avoid awkward conversations later on.
Commercial use is a different story. If that London footage is being used to sell, promote, or advertise something, it’s strongly advised to get model releases from any clearly identifiable individuals before publishing. This protects both you and the people appearing on screen and avoids any potential pesky legal issues down the line.
However, in reality, this is where filming in pubic gets a little (extra) complicated. You might be legally allowed to shoot, but practically speaking, tracking down consent from passers-by, especially on a busy London street, isn’t always easy.
This is one of the reasons many productions choose to recreate public-facing scenes in a controlled studio environment instead. In a film studio, everyone on set has given their consent, paperwork is in order, and you can focus on the creative work without worrying about who might wander into frame.