Four fire engines and around 25 firefighters were called to a flat fire on Churchill Gardens Road in Pimlico.
A fifth-floor balcony was destroyed by fire and part of a kitchen in a four-roomed flat was also damaged by the blaze. There were no reports of any injuries.
The Brigade's 999 Control Officers took 15 calls to the fire.
The Brigade was called at 1108 and the fire was under control by 1153. Fire crews from Lambeth, Battersea, Fulham and Peckham fire stations attended the scene.
The cause of the fire is under investigation.