Bike workout in London, Mayfair/Greens park area

Going to be in London all next week and can’t run/swim do to injury, so looking for a way to get in a daily ride, stationary preferred, given I’ll be in the middle of town with no independent transport. My hotel doesn’t have a fitness room and changing hotels isn’t an option, so any suggestions by locals for a nearby gym or other way to get in a spin in morning or evening?

FYI, just got back from my London trip - found out there is a Fitness First indoor fitness center on East side of Berkeley (sp?) square in Mayfair. Eight GBP per visit, but some local hotels have worked out a free deal for their guests. They have ~8 or so upright stationary bikes, and another 4 or so recumbents, along with the usual treadmills, etc. and some free weights.