Flames licked up the sides of the block in the north Kensington area as 200 firefighters, backed up by 40 fire engines, fought the blaze for hours.
Plumes of black and grey smoke billowed high into the air over the British capital hours after the blaze broke out at the Grenfell Tower where several hundred people live.
Residents rushed to escape through smoke-filled corridors in the housing block after being woken up by the smell of burning. Some said no fire alarm sounded.
Witnesses said they saw trapped residents desperately shouting for help from windows on upper floors as flames enveloped the building.
London Fire Brigade said the fire engulfed all floors from the second to the top of the block which contained 130 apartments.
"I am very sad to confirm that there have been a number of fatalities, I cannot confirm the number at this time due to the size and complexity of this building."
MORE THAN 50 TAKEN TO HOSPITAL
London Ambulance Service said more than 50 people had been taken to hospital. A witness told Reuters she feared not all the residents had escaped the fire. Some were evacuated in their pyjamas.
"I looked through the spy hole and I could see smoke everywhere and the neighbours are all there. There's a fireman shouting 'get down the stairs'," one of the block's residents, Michael Paramasivan, told BBC radio. "It was an inferno."
The cause of the fire, which broke out just before 1 a.m. (0000 GMT), was not known, the Fire Brigade said.
Residents said repairs had been made recently to the exterior of the block.
Ash Sha, 30, who witnessed the fire and has an aunt in the building who managed to escape from the second floor, said the local council had renovated the tower.
"One year ago the council renovated the building both externally and internally," Sha said.
The local council of Kensington and Chelsea, which owns the block, said its focus was on supporting the rescue and relief operation. It said the causes of the fire would be fully investigated.
More than 20 ambulance crews were at the scene. London Mayor Sadiq Khan said a "major incident" had been declared. Police closed the A40, a major road leading out of west London, while some parts of London's underground train network were closed as a precaution.
"I was just screaming at people: 'Get out, get out' and they were screaming back at me: 'We can't, the corridors are full of smoke'," he told BBC Radio.
(Additional reporting by Subrat Patnaik and Lina Saigol, Costas Pitas; Writing by Guy Faulconbridge; Editing by Michael Perry, Robert Birsel, Richard Balmforth)
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.