I've used this one a few times a short walk away from you near Tower Gateway station:-
http://www.cityoflondon.gov.uk/services/...-park.aspx
Decent multi-story, bikes a free on 1st floor undercover in their little cordoned off area. Attendant always on site manning CCTV and there's gubbins to chain bike to as well. Can be busy, but has a lot of space.
Or there's this one on Lower Thames St too:
http://www.cityoflondon.gov.uk/services/...-park.aspx
Not tried this one, but probably very similar.
It's also a good one to remember if you want to take car into town at weekend, as it's dirt cheap and close to centre.
http://www.cityoflondon.gov.uk/services/...-park.aspx
Decent multi-story, bikes a free on 1st floor undercover in their little cordoned off area. Attendant always on site manning CCTV and there's gubbins to chain bike to as well. Can be busy, but has a lot of space.
Or there's this one on Lower Thames St too:
http://www.cityoflondon.gov.uk/services/...-park.aspx
Not tried this one, but probably very similar.
It's also a good one to remember if you want to take car into town at weekend, as it's dirt cheap and close to centre.