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Six fire engines and around 40 firefighters were called to flat fire on Yarnton Way in Thamesmead.
The fire is believed to have started on the balcony and spread to the living room of the property. A woman left the affected flat before the Brigade arrived.
Around 75 residents self evacuated the block while a number of other occupants stayed inside their unaffected flats.
Part of the flat on the third floor was damaged by fire.
The Brigade was called at 2202 and the fire was under control by 2314. Fire crews from Plumstead, Erith, East Greenwich and New Cross fire stations were at the scene. The cause of the fire is believed to be accidental.