Four fire engines and around 25 firefighters were called to a fire at a flat on Cambridge Street in Pimlico.
Part of a five-roomed flat on the seventh floor of the building was damaged by fire and a small part of the window of a sixth floor flat was also damaged in the blaze. One woman and a man left the building before the Brigade arrived. One woman and two men were treated on scene by London Ambulance Service crews.
The fire is believed to be accidental and involved a candle.
A London Fire Brigade spokesperson said: "Candles are one of the most common causes of fire.
“It’s really important that you never leave a candle unattended and keep them away from anything else that can easily catch fire.”
The Brigade was called at 1849 and the fire was under control by 1930. Fire crews from Lambeth, Chelsea, Clapham and Soho fire stations attended the scene.