As far as CQB is concerned, pretty much every CQB place is limited to very small venues due to cost of buildings in the London area. I have compiled a list of all the sites that are Public Transportable and up to an hour of walking from Central London. To be honest there are very few additional sites that require a car to get to anyway and none of them CQB as far as I can say.
Outdoors, Pure Woodland or Woodland with few structures considering it's size in Green
Outdoor sites with a specific CQB section(s) of a reasonable size in Blue
Urban sites (Has a mixture of Outdoor/Woodland with significant Man made structures not purpose built for Airsoft) in Purple
Pure CQB in RED
Sites within the M25.
Bunker 51
Red 1 Chislehurst
Tactical Warfare Croydon
Mayhem Airsoft Abridge
D&A Dropzone
Incursion Airsoft "The Tunnels"
Sites just outside the M25
Reforger
Red 1 The School
Red 1 Oblivion
Ultimate Wargames
Ambush Airsoft
Campaign Airsoft
South Herts Airsoft
Sites a bit further away but possible to reach with public transport and less than an hour of walking.
Airsoft Plantation
Skirmish Billericay
Dragons Lair (Moving soon to a place that's easier to get to on public transport)
CAMO Canvey Island
Driver Wood (But the CQB specific sections are hardly used for Airsoft anymore)
Dogtag
Skirmish Wycombe
Battle Sector X
Future Survival Gravesend
Invicta Black Site **
Imperium
Splatoon
Hockley Arena
** Reachable via Train on Saturday games only, the first Sunday train is too late to arrive in time
The only pure indoor CQB sites are Bunker 51, Incursion, CAMO, Future Survival, Battle Sector X, Hockley Arena and Invicta Black Site. The largest being, Incursion and Black Site.
If you have a car than RIFTS The Battery would be well worth the trip as it is a mix of Indoor and Outdoor CQB which is pretty unique in the South East.
Splatoon is kind of urban considering a 1/3rd of the playing area is taken up by a shipping container area which is pretty good. Red 1 The School uses an old school for half the day but its very limited in terms of a playing area.