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Six fire engines and around 40 firefighters were called to a fire on Perrott Street in Plumstead.
A maisonette on the second and third floor of a four-storey block was alight. One woman left the affected maisonette before the Brigade arrived. Firefighters wearing breathing apparatus rescued a man and a woman from an adjacent maisonette via an internal staircase. All three were assessed on scene by London Ambulance Service crews.
A further 60 people left the block before the Brigade arrived.
The Brigade's 999 Control Officers took 20 calls to the fire.
The Brigade was called at 0916 and the fire was under control by 1016. Fire crews from Plumstead, East Greenwich, Erith and Eltham fire stations were at the scene.
The cause of the fire is under investigation.