Four fire engines and around 25 firefighters were called to a fire at a block of flats in Kale Road, Erith.
Part of a flat on the fifth floor and part of a balcony were damaged by fire. Forty people left the building before the arrival of the Brigade. There were no reports of any injuries.
The Brigade was called at 0731 and the fire was under control by 0814.
Fire crews from Plumstead, Erith and Bexley stations attended the incident.
The cause of the fire is under investigation.