A flat on the first floor of the building was damaged by the fire. Firefighters wearing breathing apparatus rescued one man from the affected flat. He was taken to hospital by London Ambulance Service crews.
Firefighters also rescued a man from the flat above, which was heavily smoke logged. He was rescued using a fire escape hood. Another man and woman left the building before the Brigade arrived.
Fire escape hoods provide members of the public with up to 15 minutes protection from four of the main fire gases (carbon monoxide, hydrogen cyanide, hydrogen chloride and acrolein) and can be worn by conscious or unconscious people.
If more than 15 minutes protection is required then another hood can be given to each wearer. They do not provide oxygen but temporarily filter toxic smoke to make breathing easier.
The Brigade was called at 0925 and the fire was under control by 1021. Three fire engines and around 15 firefighters from Soho and Euston fire stations were at the scene.
The cause of the fire is under investigation.