Unfortunately London has lost all its independent specialist game shops in the central tourist area. Game Focus was awesome, but it shut in 2012 iirc, I frequented it during my first year of university as it was 10 mins walk away from the central University of London campus and libraries.
However, several very good independent game shops exist in the surrounding more residential areas of London, of which I've probably visited around 15. I can't really fully recall all the names, but I'll state some rough locations that I can remember down below:
Retro Game Base on Streatham High Road (highly recommended)
A small shop called N1 Games on a side street off in Islington, near Angel Station
A shop on the Uxbridge Road (iirc) in Shepherd's Bush, right opposite the park
Games 4 U just north of Hackney Central Station (I've bought several fairly rare Wii, DS and PSP games here for a reasonable price)
A shop on Kilburn High Road, south of Kilburn Station
Games Arena in the central area of Harlesden
A shop inside the Kingsland shopping centre in Dalston
A shop on North End Road in Fulham, not far from West Brompton Station
A small shop on Burnt Oak Broadway (probably hard to find on Google, I found it accidentally one day), just north of the road with Burnt Oak Station
A shop in central Walthamstow