Southwark Crown Court heard how Philip Griffiths died in October 2014.
His brother Paul accidentally reversed into his 38-year-old sibling when the pair were trying to move a broken down scissor lift on a service road, while working for Laing O’Rourke.
Paul Griffiths tried to tow the scissor lift away using a dumper truck under the direction of managers.
During the attempt his foot got stuck between the brake and the accelerator and the truck reversed.
Philip, who was standing between the two vehicles, suffered crush injuries. He was pronounced dead at the scene.
An HSE investigation found that neither worker was authorised with the appropriate certificate to use the dumper truck, and that the operation was not properly overseen or managed.
Laing O’Rourke Construction Limited of Dartford pleaded guilty to breaching the Construction (Design and Management) Regulations and was fined £800,000 and ordered to pay costs of £10,000.
Speaking after sentence, HSE Inspector Jack Wilby said: “This incident was a tragedy for all concerned and, as revealed by our investigation, entirely avoidable.
“Laing O’Rourke did nothing to address the trend of these workers carrying out tasks they weren’t trained or authorised for.
“These dedicated staff, including Philip and his brother, needed appropriate supervision.
“Had there been appropriate supervision, then better segregation between Philip and these two vehicles could have been established and maintained.
“This case should act as a reminder of the dangers of using workplace transport without proper planning, management or monitoring of the risks involved.”
A Laing O’Rourke spokesperson said: “Laing O’Rourke fully accepts the findings of the court following the tragic events in October 2014.
“Our deepest sympathy and thoughts remain with Philip Griffiths’ family, friends and colleagues at this difficult time.
“The company is committed to continually reviewing and improving its health and safety systems.”