Six fire engines and around 40 firefighters were called to a fire at a flat on Parkside Avenue in Greenwich.
Part of a flat on the second floor of a six-storey block was damaged by the fire. Around 40 people left the building before the Brigade arrived. There were no reports of any injuries.
The Brigade’s fire investigators believe the fire was caused by an unattended candle.
A London Fire Brigade spokesperson said: “Candles, incense sticks and oil burners are one of the most common causes of fire.
"It’s really important that you never leave them unattended and keep them away from anything that could catch fire such as curtains, furniture or clothes.
"These items should always be held firmly in heat-resistant holders and placed on a stable surface where they won’t be knocked over, and make sure you put them out entirely when you leave the room and especially before bed."
The Brigade was called at 0812 and the fire was under control by 0936. Fire crews from Greenwich, Lewisham, Deptford, New Cross, Lee Green and Forest Hill fire stations were at the scene.