Operator Rick Jaeger-Fozard was killed when a Genie Z-135/70 collapsed at the Kimberly Access yard next to the M25 motorway near Heathrow last summer.
The HSE issued a safety alert earlier this week warning owners and operators that the machine must be calibrated correctly.
But Kimberly wants to see the platforms modified with an electro-mechanical safeguard to prevent the risk of human error during calibration.
The firm said: “Kimberly grounded all of its Z135/70 machines immediately following the accident, and they will be kept grounded until the company’s concerns about fundamental safety issues have been addressed and the machines have been suitably modified.
“The HSE’s Safety Alert stops short of stating what is required to prevent a similar accident occurring again.”