"Government is making money available, we're ensuring that we're going to get to the bottom of what's happened, we will ensure that people are rehoused".
He said a police investigation by specialist detectives would "establish the facts to provide, as best we possible, answers for those so deeply and tragically affected by the bad fire at Grenfell Tower".
Emergency services were called to the 24-storey residential tower block shortly before 01:00 BST on Wednesday. The toll is expected to rise.
"Finally, I would like to repeat what I have said before which is that my heart goes out, those of my colleagues, those of the wider emergency services, the community here, Londoners, and indeed everybody across this nation". "She should have been there with the residents. You have to be prepared to receive people's emotions, and not be so frightened about people", former Conservative cabinet minister Michael Portillo told the BBC.
Protesters in London accused authorities of suppressing the true death toll, an idea that has spread on social media.
In a message released on her official birthday, she said people have been "resolute in the face of adversity" following recent tragedies in London and Manchester.
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May's response has been contrasted with that of Corbyn, who hugged locals at the estate during his visit on Thursday, and the royals who met residents and volunteers earlier today.
"I appreciate that the authorities want to be absolutely certain that any information is correct before it is issued publicly, and the fire brigade, police and coroner are doing a heroic job obtaining this information in extremely hard circumstances", Sadiq Khan said. "Theresa May was here but she didn't speak to any of us".
"It will look at the building itself".
"Both myself and colleagues from London Fire Brigade have already said it will take weeks".
The officer said that the current information is based only on the number of people they believed were present inside the tower when it caught fire during the wee hours of Wednesday.
He said he was not interested in knowing why they had left it so long to make themselves known, but stressed that it was vital for police to know they are safe and well.