United Kingdom government must work quickly on an inquiry and consider tearing down similar tower blocks, says London mayor.
Building officials have not commented since the fire.
Suspicions have grown that flammable materials were used to clad the building and accelerated the spread of the fire. British media have reported that contractors installed a cheaper, less flame-resistant type of exterior paneling on the 24-story tower in a renovation that was completed just a year ago.
Police Commander Stuart Cundy says police will seek criminal prosecutions if the evidence warrants.
It includes 30 deaths that already have been confirmed, and reports of people who are missing and presumed to have been killed.
The bodies of 16 people have been taken to a mortuary, 15 who died at the scene and one who died in hospital.
One of her closest allies, Damian Green, defended May, saying she was "distraught about what has happened".
"Sadly at this time, there are 58 people who we have been told were in Grenfell Tower on the night that are missing and therefore sadly I have to assume that they are dead", he said. On Wednesday, the apartment tower caught fire, the cause of which has not been established yet.
Emergency workers have reached the 24 floor, the top floor, of the tower.
But when May went to the site of the fire Thursday, she stayed for only 15 minutes, declining to meet with any survivors or families.
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But the identification of the victims appears to be proving very hard, which experts attribute to the extreme heat of the fire.
Writing in the Observer, Mr Khan said it may well be the "defining outcome of this tragedy that the worst mistakes" of that era become a thing of the past.
Police are using the INTERPOL Disaster Victim Identification Standards to identify the dead, relying on dental records, fingerprints and DNA when possible, as well as features like tattoos or scars.
The queen and her husband, Prince Philip, stood silently on the steps of Buckingham Palace before the start of the Trooping the Color ceremony that each year marks the queen's official birthday, which is traditionally celebrated in June when the weather is warm. The queen said it was "difficult to escape a very somber mood" on what is normally a day of celebration.
The Royal Borough of Kensington and Chelsea said in a statement Friday that all residents of Grenfell Tower who had asked for help had been housed in hotels and that it was looking for interim accommodation for those people and others living nearby who could not return home. Residents want answers on why the fire spread so quickly, trapping numerous estimated 600 residents.
The government has promised a full public inquiry, but that has done little to a sense of frustration at the lack of information about how the fire moved so quickly to engulf the building. British officials have ordered a review of other buildings that have had similar renovations.
Mrs May had earlier sidestepped questions over her response to the disaster, after facing criticism of her reaction to the tragedy.
"£5 million has been made available for the immediate needs of the victims, it is being distributed". Numerous displaced are living in churches and community centers. "My commitment to families is that as soon as we can, we will locate and recover their loved ones", Cundy said.
"That's why last week's devastating tragedy at Grenfell Tower has left the nation so stunned, scared and angry", Khan wrote.