Some feared the charred tower block might collapse, but a structural engineer said the building was not in danger, the fire brigade said.
Residents who escaped spoke of others trapped and screaming for help, with some holding children from windows and others jumping from upper floors.
Twelve people died in the west London tower fire, and the number of deaths are expected to rise, police announced, as cited by BBC News.
The LondonAmbulance Service has confirmed that more than 50 people have been taken to hospitals over London.
Dany Cotton, London's Fire Commissioner who was present at the scene told reporters, "This is an unprecedented incident. This will of course be subject to a major investigation, but at this moment in time, we do not wish to speculate further about the cause of the fire, or the fire's spread".
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Grenfell Tower was built in 1974 and underwent a £10M refurbishment a year ago.
The Telegraph reported that as many as 600 people were inside the building when it caught on fire. "Somebody did, a gentleman ran forward and managed to grab the baby", Lamrani said.
Kensington and Chelsea Management Organisation came under scrutiny after it emerged a local action group had repeatedly warned about the potential for loss of life. "It's just billowing black smoke", Downey said. "In my 29 years of being a firefighter, I have never ever seen anything of this scale", she added.
Some tenants previously complained about the upkeep of the tower, specifically warning about the fire risk. Forty fire engines with 200 officers were called shortly before 1 am as flames engulfed the block from the second floor upwards "within seconds".
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.
A firemen reacts after battling a huge fire at the Grenfell Tower, a 24-story apartment block in North Kensington, London, June 14, 2017. People who live nearby were evacuated, some carrying pets in their arms as they left.
Councillor Roger Ramsey said: "Havering Council passes on its sympathies to the families and loved ones affected by the tragic incident in north Kensington and our thoughts and prayers are with all those involved".
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