The Grenfell Tower fire death toll is 12 and will rise further, Commander Stuart Cundy of the Metropolitan Police said.
People who escaped the 24-storey Grenfell Tower in north Kensington spoke of others, including children, screaming for help, some holding babies from windows and others jumping from their flats high above the ground.
London Fire Commissioner Dany Cotton said there had been a "number of fatalities" but could not say how many due to the size and complexity of the building.
She told reporters: "This is an unprecedented incident.
"In my 29 years of being a firefighter, I have never ever seen anything of this scale."
She said firefighters had only managed to get to the 19th and 20th storeys of the building.
Residents who escaped the inferno complained there had been no fire alarm, with people relying on neighbours to wake them as the blaze spread.
They said official advice in the event of a fire had been to stay inside.
Mickey Paramasivan, who was in his seventh floor flat with his partner and child, said: "If we'd listened to them and stayed in the flat we'd have perished."
London Fire Brigade said the cause of the fire was still being investigated.
But several residents reported one man had said it started in his faulty fridge.