I'd be surprised if you can get access to buildings in London (or any city for that matter) to run up and down the stairs.
There are issues about health and safety and liability in the event you fall, or run into someone who's just trying to go to another floor, plus security/terrorism issues around letting people into buildings in the capital.
The tower blocks at hospitals have stairways which are generally accessible to all. Great training when 'im indoors was incarcerated on the 10th floor of St. Thos's for a month and I visited him twice daily. Best not to make yourselves too noticeable though.
Comments
I'd be surprised if you can get access to buildings in London (or any city for that matter) to run up and down the stairs.
There are issues about health and safety and liability in the event you fall, or run into someone who's just trying to go to another floor, plus security/terrorism issues around letting people into buildings in the capital.
Vertical Rush London
there's also a link to Vertical World Circuit which might have more info you're looking for - interesting links page as well