The evacuation of people from the Grenfell Tower block remained ongoing, according to police.
London Fire Commissioner Dany Cotton told reporters: "This is an unprecedented incident".
"It's the most terrifying thing I've ever seen".
The building is at least 24 storeys high.
A local building expert has told LBC that he voiced concern over the fire risk at Grenfell Tower.
There was no immediate word on the cause of the blaze, but angry residents said they had warned local authorities about fire issues at Grenfell Tower.
"We've complained to council", said Edward Daffarn, 55, who said nothing had been done to improve safety.
The cause of the fire was not known at this stage, London Fire Brigade said.
But several residents reported one man had said it started in his faulty fridge. "I've not heard from them since, the phone is not going through, the landline isn't going through", she said.
"We have declared a major incident and continue to work closely with other emergency services at the scene".
Pictures from the scene showed flames engulfing the block and a plume of smoke visible across London, while others showed residents looking out of windows in the block.
People in apartments enveloped by the quickly advancing flames and thick smoke banged on windows and screamed for help to those watching down below, witnesses and survivors said.
"About 12 floors up I saw three children waving from a window and then there was just an explosion and they disappeared".
"I went inside, grabbed my little girl and my girlfriend, and ran".
"Our advice has always been if there is a fire stay in your flat, but if we had stayed in that flat we would have been perished".
"It was like something out of a disaster movie".
"I walked out into the common area to see if the lifts are moving, to see if people are in a hassle - nothing".
No confirmation has yet been made on any deaths in the fire.
Actor and writer Tim Downie, who lives around 600 metres from the scene in Latimer Road, said: "It's horrendous".
The blaze, which broke out at 1am, engulfed the whole building at a time when hundreds of people were inside.
After the fire, the group posted: "All our warnings fell on deaf ears and we predicted that a catastrophe like this was inevitable and just a matter of time".
A London fire survivor said flames shot up Grenfell Tower "like a match-stick" due to flammable cladding.
George Clarke, the presenter of Channel 4 TV program Amazing Spaces, told Radio 5 Live, "I'm 100 meters away and I'm absolutely covered in ash". I just hope they have got everyone out. She says firefighters are still working and she can't say how many people may have died. "Just complete nightmare, absolute nightmare", recounted Littlejohn.
"As I was going down the stairs, there were firefighters, truly wonderful firefighters that were actually going upstairs, to the fire, trying to get as many people out the building as possible", he told the BBC.