The alarm was raised at 11am yesterday morning when the fire was spotted on the roof of the 10-storey building, which is being converted into luxury flats and a hotel.
Workers were evacuated from the site as firefighters battled to get the blaze under control at the Old Marconi House building.
More than 75 fire fighters and 15 engines spent two hours tackling the rooftop fire.
A spokeswoman for Galliard Homes, said: “We can confirm that all the staff and workforce were evacuated safely. The damage appears to be limited to the central section of the roof near the Montreal Place elevation.
“We are now awaiting further reports from the fire service.”
A London Fire Brigade spokesman could not confirm the cause of the blaze but said investigators would be interviewing workers. He said the workers’ tools would be one line of inquiry.
The LFB spokesman said the fire took hold of about a quarter of the 100 sq m roof of the landmark building, which is currently being converted to a design by Norman Foster’s architectural firm.