Four fire engines and around 25 firefighters were called to a maisonette fire on Overhill Road in East Dulwich.
Part of a maisonette on the fourth floor of a 12-storey block was damaged by the fire. There were no reports of any injuries.
The cause of the fire is believed to have involved cooking.
A London Fire Brigade spokesperson said: "Fires are more likely to start in the kitchen than any other room in the home.
"Cooking should never be left unattended on the hob or grill - if you have to leave the kitchen, turn off the heat.”
The Brigade was called at 1154 and the fire was under control by 1237. Fire crews from Forest Hill, New Cross and Brixton fire stations were at the scene.