Actually, no Roman legions appear to have been based in London.
There was a fort in the north-west of the Roman city, built early in the second century, which could have held a garrison of about 1000 soldiers. However, this was the guard available to the governor of the province, rather than any particular legion.
In fact, five legions are known to have served in Britain:
- Legio II Augusta - Based at at Glevum (modern Gloucester), and later at Isca Augusta (modern Caerleon)
- Legio VI Victrix - Based in the north of the province, and eventually stationed at Eboracum (modern York)
- Legio IX Hispana - Based at the fort of Lindum Colonia (at Lincoln), and later at Eboracum (modern York)
- Legio XIV Gemina - Based at the legionary fortress at Mancetter on Watling Street. Moved to the Balkans in 67 AD
- Legio XX Valeria Victrix - Based at Camulodunum, Usk, and Viroconium (Wroxeter), before moving to Deva Victrix in the City of Chester.
Of the legions known to have served in Britain, Legio II Augusta, Legio IX Hispana, Legio XIV Gemina, and Legio XX Valeria Victrix were involved in the Claudian conquest of the province, while Legio VI Victrix was relocated to Britannia by the Emperor Hadrian in 119 AD.
None of these legions are known to have been based in Londinium at any time.
As a point of interest, the best-surviving part of Londinium's Roman Fort is its western gateway, which is preserved within a car-park under London Wall (the road):
Visit's are arranged by the Museum of London (usually with free entry on Open House London weekends).