Fifteen fire engines and around 100 firefighters were called to a flat fire on the A5 in Maida Vale.
A flat on the fifth floor of the building was destroyed and half of the fascia of a flat on the sixth floor was damaged by fire.
Station Commander Emma Carr, who was at the scene, said: “Firefighters worked hard to bring the fire under control.
"Our Control Officers took more than 20 calls to the fire and gave vital fire survival guidance to two residents inside the building on how to stay safe before crews arrived.
"Firefighters wearing breathing apparatus led 24 people to safety, including 15 using fire escape hoods. London Ambulance Service crews treated nine people on scene and seven people were taken to hospital.
"One of the Brigade's 32-metre turntable ladders was used as a water tower to tackle flames from height.
"The wind was causing smoke to spread across the area. People who live or work nearby were advised to keep windows and doors closed."
London firefighters were among the first in the UK to carry fire escape hoods when they were introduced in 2018 as part of improvements following the Grenfell Tower fire. The hoods provide members of the public with up to 15 minutes protection from four of the main fire gases (carbon monoxide, hydrogen cyanide, hydrogen chloride and acrolein) and can be worn by conscious or unconscious people. If more than 15 minutes protection is required then another hood can be given to each wearer. They do not provide oxygen but temporarily filter toxic smoke to make breathing easier.
The Brigade was called at 0938 and crews from Paddington, West Hampstead, North Kensington, Euston and surrounding fire stations attended the scene. The fire was under control by 1205.
The cause of the fire is under investigation.