Four fire engines and around 25 firefighters tackled a fire on St John's Hill in Battersea.
Half of the second floor and part of the third floor of an end-of terraced house converted into flats was damaged by fire. There were no reports of any injuries.
The fire is being treated as accidental and is believed to have been caused by cooking left unattended.
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 1721 and the fire was brought under control by 1853. Crews from Battersea, Wandsworth, Clapham and Lambeth fire stations attended the scene.
Practical steps for safer cooking
· Take extra care when cooking with hot oil as it can easily overheat and catch fire.
· Never fill a pan more than one third full of fat or oil.
· Make sure food is dry before putting it in hot oil – oil and water are a dangerous mix.
· If the oil starts to smoke, it’s too hot. Turn off the heat and leave it to cool.
· Try not to leave cooking unattended on the hob or grill – if you have to leave the kitchen, turn off the heat.
· Not feeling 100%? Order a takeaway – if you're very tired, have been drinking alcohol or are taking medication that might make you drowsy, it's safer not to risk it.
· Be fabric aware – loose clothing can easily catch fire, so take care not to lean over a hot hob, and always keep tea towels and cloths away from the cooker and hob.