BJJ is a notoriously expensive martial art, and Gracie franchises especially so. For something like Taekwondo, Judo, or Karate you're looking at more like £80-100 per month for 2-3x weekly classes. And for a lot of team sports it'll be considerably less. I competed both in Taekwondo sparring and ultimate frisbee as a student, and both were easy to do on the cheap.
Also I think OP was confused by what you meant by "gym". In the UK that normally refers just to a place with weights and cardio machines. One of the most popular chains is Pure Gym which is typically around £30 per month: https://www.puregym.com/city/central-london/
We've just signed up to a more expensive gym with a pool, spa, sauna, etc..., but it's still around £160 per month for us as a family in South-West London.
