Grief turned to outrage Friday amid reports that materials used in the building's renovation could have fueled the i.
Some 600 people were living in the tower's 120 apartments.
The Guardian newspaper reported that contractors installed a cheaper, less flame-resistant type of panelling in the renovation that ended in May 2016.
On the figure of 58, he said: "I really hope it won't, but it may increase", while adding that "it might be that some of those are safe and well", and for some reason, had not yet made themselves known to the police.
At least 30 people were killed in Wednesday's inferno, which left Grenfell Tower a charred hulk.
The recovery operation at the burnt-out block of flats has resumed and could take weeks, Cundy explained and May said she expected to announce the name of the judge for a public inquiry within the next few days.
"I have heard the concerns and I have ordered immediate action across the board to help victims' relatives and the survivors", May said.
Police Commander Stuart Cundy says police will seek criminal prosecutions if the evidence warrants.
One of her closest allies, Damian Green, defended May, saying she was "distraught about what has happened".
Authorities in London said Saturday that 58 people missing are presumed dead from this week's fire disaster at a high-rise tower. Cundy said emergency workers have now reached the top of the building. The group left after a meeting that lasted more than two hours but did not speak to reporters gathered outside.
May also said that she has set a deadline of three weeks for all the survivors of the Grenfell fire to be placed in new housing.More news: Nicola Sturgeon grilled over education record during election event
The London mayor also said the response from Kensington and Chelsea Council has "not been good enough".
Families who have lost their homes must be supported, he added, grieving people must be helped and lessons must be learned following the tragedy, including ensuring it is not "so hard" for those who need help to find it.
Earlier in the day, Scotland Yard expressed fears that all the victims of the massive fire may never be identified.
"This is an absolutely bad fire that took place".
Opponents said Mrs May's handling of the fire has thrust her position further into doubt.
Officials are using dental records, fingerprints, DNA samples, tattoos and scars to try and positively identify victims.
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.
"Put to the test, the United Kingdom has been resolute in the face of adversity", the queen wrote in her message.
In a television interview Friday, she sidestepped questions over whether she had misread the public mood.
Local residents have decried inadequate information and aid from council staff in the fire's aftermath, with hundreds of disgruntled demonstrators flocking to protest at Kensington town hall Saturday.
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.
She described the Grenfell Tower blaze as "an unimaginable tragedy for the community, and for our country". More than three million pounds ($3.8m) have been raised for the affected families.