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I would like to know if there are any groups for tower runners. Also what towers in London can you have access to at any time to do tower running?
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.