Fashion East, a project aimed at helping to nurture emerging young designers through the difficult early stages of their career, receives sponsorship funding from high street fashion chain Topshop, Topman and the Greater London Authority.
Topshop said it did not stop the show because the builder was dealt with immediately.
A spokesman said: "We're aware that people are asking why we didn't stop the show. As soon as we realised what had happened, medical staff and production security were taking care of him.
"The builder was working on an adjacent building site to the Topshop show space and walked on the corrugated glass roof on top of the space - as to why he walked on it we do not know yet - but the slate of glass gave way. He fell in an area to the back of the stage."
The London Ambulance Service was alerted about the accident at 1.18pm.
A spokesman said: "We sent an ambulance crew and London's Air Ambulance to the scene. We treated a man reported to be in his 30s for a back injury.
"He was taken to The Royal London Hospital, as a priority, by road ambulance, escorted by the doctor from London's Air Ambulance."
This isn't the first instance of catwalk-related drama.
In 2005, Hilary Alexander, then Fashion Director of The Daily Telegraph, narrowly escaped injury when lights at New York designer Diane Von Furstenberg's spring/summer 2006 show fell from the ceiling.
And in 1999 photographers boycotted a Jean Paul Gaultier because of working conditions that they deemed to be unsafe.
- Indpendent