"The investigation will look in into what criminal offences may have been committed", Metropolitan Police Commander Stuart Cundy said.
Asked if the final figure would be double or triple digits, Mr Cundy said: "I'd like to hope that it isn't going to be triple figures".
Residents said refurbishment work had recently been carried out with work on the gas supply to the flats. Thirty-seven people remained in hospital, with 17 of them in critical care.
Home Office Minister Nick Hurd described the Grenfell Tower fire as a "national tragedy" and said a full search was "unlikely to be feasible for some time". But the shock at its scale turned to anger and recriminations today.
Firefighters trying to race into the building were protected from the falling debris by police officers who placed riot shields over their heads.
Mr Corbyn also said hundreds of thousands of people living in tower blocks will be "frightened, traumatised and very, very worried" following the blaze in west London.
Many fire experts have pointed to the cladding as a likely factor in how the fire spread so quickly up the 24-story building.
"I'm able to say at this point in time at least 30 people have died as a result of this fire", he said.
"As I've said, we need to do whatever it it takes to either make those properties safe or find alternative accommodation. People deserve answers; the inquiry will give them".
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City councilwoman Jenni McCauley said the tight-knit community was "thrilled" to have Warmbier back. An examination revealed that he has "extensive loss of brain tissue in all regions of the brain".
"The severity and the heat of the fire will mean that it will be an absolute miracle for anyone to be left alive", she said as she indicated that the search operation could take weeks. "We will demand and get answers".
"Families must not face the indignity of having to hand over reams of personal and financial paperwork - which a lot of them will no longer have for obvious reasons - to the overworked and bureaucratic Legal Aid Agency", she said.
"We tried the door but it was too hot", the 39-year-old told The Sun. Khan replied that firefighters were still searching the building. Londor Mayor Sadiq Khan also visited the area.
A Cabinet minister has admitted that any parent would be anxious about putting their children to bed if they were living in a high-rise building like Grenfell Tower.
Others gathered seeking news of the missing.
She was told some residents wished she had spoken to them and visited community centres offering support. "The phone was ringing but they didn't reply to us". We were from the same community, and many in the tower were. "Maybe 70 percent are from Somalia, Sudan, Morocco". And from my colleagues within the health service, there are still a number of people who are receiving treatment in hospital. Residents of the tower had repeatedly warned local officials that the building was a firetrap and that a "catastrophic event" was inevitable.
The tower block fire was finally put out this morning as courageous firefighters risked their lives to wade through the inferno.
Outside the security cordons around the base of the tower, impromptu tributes appeared, with photos of missing people, messages of condolences and flowers.
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