The London Fire Brigade said the fire was reported at 2.44am on Monday (11.44am AEST) and the entire building was affected, including scaffolding surrounding the property and the roof.
The building has been evacuated and a significant search and rescue operation is under way.
The London Ambulance Service said four people were treated at the scene and two were take to the hospital.
As many as 40 fire engines and about 225 firefighters responded to the fire at the building, which has both residential and commercial units. The cause of the blaze isn’t yet known.