May made the announcement while speaking to survivors of the fire that on Wednesday ripped through the 24-story Grenfell Tower in Kensington while most residents were sleeping, leaving dozens dead, of which 30 have been found and identified, and hundreds homeless.
London Fire Commissioner Dany Cotton said her crews had identified a "number" of those killed, "but we know there will be more".
Earlier on Saturday Prime Minister Theresa May met victims of the blaze at Downing Street, amid criticism she had not seen them in the immediate wake of the tragedy.
Kensington and Chelsea Town Hall became another flashpoint on Friday with protesters storming the building, accusing authorities of ignoring them and of forcing low-income families to live in sub-standard housing.
Ms May says she "spoke with people who ran from the fire in only the clothes they were wearing".
Residents of the destroyed tower said May was far too slow to visit the stricken community, that the building had been unsafe and that officials have failed to give enough information and support to those who have lost relatives and their homes.
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BBC Newsnight reports that the type of cladding on the outside of Grenfell Tower, installed in 2015 during a refurbishment, had a polyethylene - or plastic - core, instead of a more fireproof alternative with a mineral core.
"There's a need for the public to hear you say in words of one syllable: 'Something bad has happened; something has gone badly wrong".
"Everyone affected by this tragedy needs reassurance that the Government is there for them at this bad time - and that is what I am determined to provide".
"I said 'where are you?' He said 'I'm in the flat, '" Ali said. I spoke with people who ran from the fire in only the clothes they were wearing.
"We are not here to trouble people". Currently, 30 people have been confirmed dead, and there are 70 people unaccounted for.
"Afterwards, she will meet a group of residents, victims, volunteers and community leaders in Number 10".
Similar demonstrations are being held across the United Kingdom and Ireland in answer to a call from the residents in Grenfell urging people to help demand justice for the victims who perished in the fire, their families and all those affected.