Dozens of people remain missing.
St. Clement's Notting Dale, a church near the tower, has turned into an informal center for people searching for missing friends and family. Those who escaped were offered housing overnight. "They feel the government and local council haven't done enough to help them".
Seventy-four people were being treated in hospitals, 20 of them in critical condition.
The announcement to probe the incident came after London Mayor Sadiq Khan demanded an urgent investigation into the tragedy.
Firefighters were still working to dampen the blaze and search for remains of the dead Thursday.
Fire at London high rise built in 1974 killed six people. I wanted a briefing from the emergency services.
Residents and victims have expressed outrage at Prime Minister Theresa May, who visited the site the day before without meeting with local residents.
London police said Friday that 30 people are known to have died in the blaze that started just before 1 a.m. Wednesday, surprising many people as they slept.
The announcement of probe comes after Labour MP David Lammy argued that the Grenfell Tower fire amounts to "corporate manslaughter, and led calls for a criminal investigation into the issue".
Communities Secretary Sajid Javid told the BBC on Friday there would be immediate action following early conclusions from an investigative report into the fire.
Ms Cotton suggested it "will take weeks before this building is truly cleared and searched properly" as parts of it still need to be shored up and there is a risk of falling debris.
"She said "Mum where are you?"
More than 200 firefighters worked through the night.
Harley Facades, which completed the refurbishment work, said in a statement: "At this time, we are not aware of any link between the fire and the exterior cladding to the tower".
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Notably, redevelopment of the building included provisions for improvements to the "smoke/fire safety and ventilation works".
"There is no way that rich people live in a building without adequate fire safety".
A series of fires around the world have heightened concern that cladding systems are providing both a means for fire to spread through buildings.
Anthony Blakemore, a Londoner who like Adele visited Grenfell Tower last night, said on Twitter that "the strength of the community spirit restored my faith in humanity".
"We will cooperate with the relevant authorities and emergency services and fully support their enquiries into the causes of this fire at the appropriate time", it said.
"We are aware that concerns have been raised historically by residents".
Wayne Brown, London Fire Brigade Deputy Assistant Commissioner, said in 25 years on the job he had "never seen a fire with that intensity spread so quickly throughout a building of this size".
Her announcement came amid calls for corporate manslaughter charges to be brought following the disaster, as Scotland Yard confirmed it was investigating the cause of the blaze.
He said: "Without us realising one of my young children had put a pencil inside the radiator; I dealt with it personally and managed to put it out".
According to the government's website, a full plans decision notice is "the most thorough option", but this was not taken.
"It is considered that occupants are safer in their dwelling than coming out into potentially smoke logged corridors", he said.
Opposition leader Jeremy Corbyn, who visited the tower block on Thursday after the prime minister, said, "some very hard questions must be answered".
"The best thing about today has been seeing how generous people are", charity worker Zain Miah told CNN.
She added: "What we need to do is ensure that this bad tragedy is properly investigated".
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