People in the north Kensington tower block were trapped overnight with witnesses describing seeing a mother throwing her baby out of a window and others jumping from flats.
"The baby just sort of dropped in a straight line, and a guy just ran forward and the baby fell into his arms", she said. "It had completely spread within half an hour".
More than 50 people were injured and taken to hospital following the blaze at Grenfell Tower, where several hundred people lived.
Authorities say 65 people were rescued from the blaze. "They were also providing food and clothes to people".
"There were even young children banging on the windows", she told CNN, adding she could hear screams as the hours went by. "They were running and telling people".
London Fire Commissioner Dany Cotton has confirmed that police were first called at 12.54, before the first of 40 units arrived within six minutes.
"Currently, we're focusing on helping those residents and London Fire Brigade is investigating the safety of the tower's structure but we will issue a further statement in due course", said Robert Black, the company's chief executive. She sat with her grandson outside the building, helplessly watching those trapped on higher floors.
Those trapped in the tower - some of whom remain inside nearly 12 hours later - were heard begging for their lives, waving towels, torches and mobile phones in hopes of alerting the 200 firefighters on site of their whereabouts.More news: Sony, Microsoft, Nintendo to make major announcements at E3
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Eerie photos have emerged from a nearby building where people flocked as 22 floors next door were gutted by the inferno.
Nassima Boutrig, who lives opposite the building, said she was awakened by sirens and smoke so thick that it filled her home. "We could see a lot of children and parents screaming for 'Help!"
Details on how to help the victims can be found here. It was fire up, up, up. "They couldn't stop the fire".
The major fire comes just 10 days after a terrorist attack occured in the city.
Cundy said an extensive area was sealed off around the decimated building, which was engulfed in flames in most parts from the second floor up to the roof.
"I'm lucky to be alive".
"There were no fire alarms", said Edward Daffarn 55, who was warned by a neighbor to flee. "I consider this mass murder".
"This matter is of particular concern as there is only one entry and exit to Grenfell Tower during the improvement works", read a blog post by the Grenfell Action Group.
In a blog on November 20, the activist group predicted that only "a catastrophic event" leading to "serious loss of life" would bring the outside scrutiny needed to make conditions safe for residents. The cause of the fire was not immediately known. We will cooperate fully with all the relevant authorities in order to ascertain the cause of this tragedy.
Grenfell Tower has 120 apartments on 24 floors, including 20 residential levels and 4 community levels.