The Health and Safety Executive said the top five contractor had “failed to make adequate risk assessments and plan a safe system of work” on the project – Europe’s largest regeneration development.
Liverpool Crown Court heard employee William Taylor fell more than 3 m during the construction of concrete stairs inside one of the main apartment blocks on the project.
HSE principal inspector Nic Rigby said Mr Taylor sustained multiple serious head and other injuries and narrowly escaped falling three floors to the base of the building. The court was told that two other workers also escaped injury whilst working in the same unprotected area.
Mr Rigby said: "This prosecution should act as a warning to all those involved in the management of construction work. It was down to chance alone that this incident did not result in a fatality. That risk would have been avoided had the planning and management of the work being carried out not been so deficient.
He added: "The accident occurred because the company failed to make adequate risk assessments and plan a safe system of work. This accident happened on the third floor of the building.
"Had the accident not occurred this same system of work would have been repeated on every one of the 12 floors of the building. A fall from that height would clearly have had much more serious consequences."
A Laing O'Rourke spokesman said the company "has learned and will continue to learn lessons from this incident".
He said: "Laing O’Rourke Construction has been and will continue to be fully committed to the health and safety of all its employees, contractors and the general public."
The company – which was fined £80,000 and ordered to pay £10,000 in court costs – pleaded guilty to a breach under the Health and Safety at Work etc Act.