Four fire engines and around 25 firefighters were called to a flat fire on Putney Hill in Putney.
Part of the kitchen of a fourth-floor flat was damaged by fire. One woman left the property before the Brigade arrived and was treated on scene by London Ambulance Service crews.
The fire is believed to have been caused by cooking that was left unattended.
Sub Officer Matthew Mayes, who was at the scene, said: “Crews worked incredibly quickly to access the property and bring the fire under control and stop it from spreading to other flats.
“The fire started after cooking was left unattended and spread into the extractor fan.
“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 1303 and the fire was under control by 1348. Fire crews from Wandsworth, Battersea and Hammersmith fire stations attended the scene.