The fire is believed to have started at around 1am this morning at the Grenfell Tower in North Kensington.
The huge fire quickly spread through all but the first two floors of the building and people inside could be seen waving for help.
A spokesman for the London Ambulance service has said so far 30 people have been taking to hospital and they still have around 20 ambulances on the scene.
Thick black smoke continues to pour from the building six hours after the fire first broke out.
It is feared that some people may still be trapped inside.