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Eight fire engines and around 60 firefighters were called to a fire at a commercial and residential building on Laban Walk in Deptford.
A small section of a laundry room on the first floor was damaged by fire.
One man was led to safety from the third floor via an internal staircase by firefighters wearing breathing apparatus.
A further 20 people left the building before the arrival of the Brigade.
Three men and three women were assessed at the scene by London Ambulance Service crews.
The Brigade was called at 2253 and the fire was under control at 0020. Fire crews from Deptford, Greenwich, New Cross and surrounding areas fire stations attended the scene.
The cause of the fire is under investigation.