Apprentice Sunny Holland had been working for Andrew Geer Scaffolding for eight months before he fell 6.5m while working on Whitehall Court in Horse Guards Avenue, Westminster on 24 April.
The 20 year old from St Mary Cray was taken by ambulance to intensive care at the Royal London Hospital, Whitechapel. His life support was switched off the following day because of the severity of his brain injuries.
The family were later told by the Kent-based firm they would have to fork out thousands for his funeral because Mr Holland had been employed under CIS, which effectively means workers are self-employed and are responsible for their own insurance.
An Ucatt spokesman said: "About half of the construction industry hire staff under CIS so if a tragedy happens, it can mean that workers are not insured. It is a huge problem. We have to deal with this all the time.
"People who are employed under CIS are usually more vulnerable to accidents and even death because work is more casualised and there is not so much of a duty of care to the worker."
He added: "Our advice to all workers working at height is that they should wear a harness at all times.
Mr Holland’s aunt Judith Young said the news regarding the insurance had been a further blow to the family.
She said: "They've told us that he wasn't insured so I have been walking around the streets raising money for his funeral, it is pitiful really.
"Since the accident, the company has not said anything about what actually happened to Sunny and nobody has come round to see us. We are so raw and are just trying to take it all in."
Andrew Geer Scaffolding was unavailable for comment.