Indoor climbing

Assuming you live in Brighton then your pick of London gyms isn't area specific?

In that case for purely bouldering I would check out Yonder. It's only been open a couple of months but honestly the place is just beautiful. Aesthetically it cannot be beaten. Everything has been custom fabricated with such fine attention to detail. The hold sets (+ colour, grade numbering system) are awesome. The wall angles and texture are unique. I particularly like the huge circuit board with user adjustable angle and laser cut panelling. Also a yoga studio, great cafe with pool table and Beavertown on tap for post-sesh recovery gainz.

The setting is good but is matched at Stronghold (two amazing top out boulders, loads of climbing but lacking a roof), Vauxwall (outdoorsy which is a good thing, but the West centre can be claustrophobic so try the East first) and Mile End (a particularly wicked set of proper comp holds+volumes on their comp wall and an outdoor style faux-rock boulder).

The Castle is amazing too and the place to go if you want bouldering, top rope and lead all in one place. It's particularly busy on weekday evenings but the history and quirky layout of the Victorian pump house makes it really fun.

For rope climbing only the Westway is very spacious and has good setting too.