Here's a list of improv friendly rehearsal spaces in London that don't cost too much:
The Rag Factory, ragfactory.org.uk: Lots of different rooms. Silas the owner is very supportive of improv groups and sometimes discounts on smaller rooms or off-peak nights. Good location near Brick Lane too.
The Nursery Training Centre, thenurserytheatre.com: Two lovely rooms. Very supportive of improv as it's run by Jules Munns, who runs both The Nursery and The Slapdash Improv Festival. Great location in London Bridge.
The Miller, themiller.co.uk: The pub where we run our shows, also has a smaller basement studio for rehearsals and the upstairs room can be rented during the day.
Calder Bookshop Theatre, calderbookshop.com: Surprisingly cheap space considering it's so close to Waterloo.
Theatre Delicatessen, theatredelicatessen.com: Lots of rooms in Farringdon, various improv groups practing there.
The Cockpit Theatre, thecockpit.org.uk: Various rooms and good prices in Marylebone.
The New Diorama Theatre, newdiorama.com: We haven't used this yet but have heard it's reasonably priced.
Sitting Rooms: If you have understanding neighbours, or no neighbours, you can always rehearse in one of your team's sitting room. It works quite well and can be more sociable, bring some snacks and drinks over.
Office Space: Using one of the team member's office space meeting rooms after hours is also a popular choice.
Rooms above pubs: Many pubs have spare rooms you can sometimes get for free or cheap so it's worth asking around.
There are lots more but we thought we'd keep it simple and just include the ones that tend to get used most for improv. If we've missed any please let us know (firstname.lastname@example.org).