The tower crane toppled on to an apartment block at Chandlers Wharf in Liverpool city centre in July 2009.
Merseyside crane driver Iain Gillham, 54, was paralysed from the waist down after he was flung from the crane.
He had to be rescued from the roof of the adjacent building to the wharf site, suffering a fractured skull, spine fractures, broken shoulder and brain haemorrhage.
The 200t tower crane he was operating was being used to help build a new hotel and apartment blocks at Kings Dock Mill, on Tabley Street.
The case, which opened at Liverpool Crown Court yesterday, is expected to run for three weeks.
Both firms deny breaching health and safety laws in connection with those other than their employees.
B&K also pleaded not guilty to failures in connection with an employee.