Six fire engines and around 40 firefighters were called to a fire at a flat on Glyndon Road in Plumstead.
An enclosed balcony on the 23rd floor of the building was destroyed by fire. There were no reports of any injuries.
Station Commander Verona Clarke, who was at the scene, said: "Crews worked incredibly hard to stop the fire from spreading and causing further damage to surrounding flats."
The Brigade's Fire Investigators believe the fire was caused by an unattended candle.
Firefighters' top tips for safe candle use
- Make sure you put out any candles, incense and oil burners when you leave the room and especially before bed.
- These items should always be held firmly in heat-resistant holders and placed on a stable surface where they won’t be knocked over.
- Keep them away from materials that might catch fire – that's things like curtains, furniture, clothes and hair.
- Be especially careful if you have a lot of flammable items in your home, like collections of books, magazines or papers.
- Be aware that tea lights get very hot and without proper holders can melt through plastic surfaces like a TV or bath.
- To avoid accidents keep candles and other naked flames out of reach of children and pets.
The Brigade was called at 1520 and the fire was under control by 1609. Fire crews from Plumstead, Erith, Eltham, Bexley and surrounding fire stations attended the scene.