Off the top of my head:
London Snooker (Tooting)
Spots & Stripes (Redhill)
Raging Ball (St Albans, Greenford and High Wycombe).
Spots and Stripes plays host to two GB9 tour stops a year. Slightly outside of London but good set-up.
London Snooker hosts "London's Finest" pool events.
Raging Ball actually advertised on Google as a bingo room. However, High Wycombe and St Albans clubs were both very nice clubs to play in, pre-covid.
I used to co-run events from a Rileys club in Solihull (100 miles north of London). They offer discount rates to students, who abuse the tables. Then they charge top whack to serious players who bring their own cues, balls, chalk and racks.