In London, it depends on what you're actually doing in the room. Premises offering "special treatments" such as massage, manicures, pedicures, facials, nails, laser or light work and electrolysis must hold a Special Treatment licence from the borough council under the London Local Authorities Act 1991, and
CNHC is clear that operating without one is illegal.
The borough issues that licence, and applicants typically need to show proof of public liability insurance, as
Westminster City Council sets out.
Here's the nuance worth knowing. The licence is tied to the licensable treatments being performed, so a pure photo shoot or a pop-up with no treatments may not need one at all. Rules and thresholds vary by area, so check directly with the borough where the space sits before you book.
Pro tip: Book a Peerspace salon and the venue side is the host's job, so for shoots and pop-ups you're not the one wrangling premises paperwork. Just remember that if you're performing licensable treatments yourself, your own licence and cover are still on you.