Six fire engines and around 40 firefighters were called to a flat fire on St Anns Road in Holland Park.
Firefighters wearing breathing apparatus led one man to safety. London Ambulance Service crews treated a number of people at the scene.
The Brigade's 999 Control Officers took 22 calls to the blaze and gave survival guidance to residents while they waited for firefighters to arrive.
The fire is believed to have started on the balcony and spread to a flat on the second floor.
The Brigade was called at 1945 and the fire was under control by 2103. Fire crews from North Kensington, Hammersmith, Kensington, Paddington and Soho fire stations were at the scene.
The cause of the fire is under investigation by the Brigade and London Metropolitan Police Service.