Five fire engines and around 35 firefighters tackled a flat fire on Yarnton Way in Thamesmead.
Most of a four-roomed flat on the 12th floor of a 13-storey block of flats was damaged by the fire. Ten people from neighbouring flats and a cat were led to safety by fire crews. There were no injuries reported.
The Brigade was called at 0924 and the fire was under control by 1053. Fire crews from Plumstead, Erith, Bexley and East Greenwich fire stations were in attendance.
The cause of the fire is under investigation.