Westminster Magistrates' Court was told that a crane operator was lifting a pack of scaffolding tubes on to a platform with the assistance of a slinger signaller.
The driver had a restricted view of the load and it struck the side of the platform. The poles spilled on to a gantry two storeys below, injuring a scaffolder who was working there.
BAM Construction pleaded guilty to breaching s 8(1) of the Lifting Operations and Lifting Equipment Regulations, which requires employers to properly plan and supervise a lifting task and ensure it is carried out safely.
It was fined and ordered to pay £8,700 costs.
After the accident on 9 December 2015, BAM Construction enhanced its existing measures to control access to nearby areas during the lifting of loads, the Health and Safety Executive (HSE) said.
HSE inspector Stephron Baker Holmes said: "Construction companies should think carefully about how best to prevent loads being lifted over people who may be working in areas nearby. In some cases it may be possible to restrict access to a particular area while lifting operations are being carried out above."