Firefighters are still tackling the blaze at Grenfell Tower in north Kensington, where hundreds of people are thought to live.
Eyewitnesses reported seeing people trapped inside their homes.
The BBC's Andy Moore said the whole 24-storey block had been alight and there were fears the building might collapse.
Eyewitnesses said they saw lights - thought to be mobile phones or torches - flashing at the top of the block of flats, and trapped residents coming to their windows.
The Met Police has set up an emergency number on 0800 0961 233 for anyone concerned about friends or family.
At 06:15 BST, London Ambulance Service said 20 ambulance crews had been at the scene, 30 people had been taken to hospital, but the nature and level of their injuries was not yet clear.
Mayor of London Sadiq Khan said a "major incident" had been declared.
Three hours after the fire started, police said people were continuing to be evacuated from the tower.