The staircase demolished a boundary fence and bounced off a heavily used site footpath before coming to rest near some workers on the Canary Wharf site, which is now 20 Canada Square.
Health and Safety Executive inspector Andy Beal said: "It's remarkable that nobody was seriously injured or killed when this heavy staircase hit the ground.
It was dropped because of shortcomings in Cleveland Bridge's design of the lifting equipment used, in the training of its staff and the monitoring of lifting operations.
"Any firm carrying out lifting operations must plan the work properly and communicate effectively with their workforce."
Cleveland Bridge was also ordered to pay £4519 in costs.