They also complained that May's visit to the neighborhood was too slow and that support was lacking for those who lost relatives and homes.
Theresa May was so moved by the stories of Grenfell victims during her meetings with them this weekend that she was "welling up", according to a reverend who was there.
The PM has said the support for families was "not good enough" in the hours after the disaster.
Chair of the National Fire Chiefs Council, Roy Wilsher, said if the fire spread up the outside of the tower, sprinklers might not have made a difference.
"And our priority is to bring out those who are still in there".
Although police did not speculate on the eventual number of fatalities, local community sources say at least 70 from Grenfell Tower are still missing, including entire families.
Metropolitan Police Commander Stuart Cundy said Thursday of the toll: "I'd like to hope that it isn't going to be triple figures". "But it would also be deeply distressing for families for us to release wrong information". On Saturday, NHS England said 19 people were being treated in hospital, with 10 in critical condition.
"That number 58 may change".
The upper floors of Grenfell Tower sustained significant damage, he says, and "the sad reality is that this work will take some time, stretching into many, many weeks". But it may increase.
London fire: Death toll rises to 58
On Saturday, NHS England said 19 people were being treated in hospital, with 10 in critical condition. It does not matter why you have not told us, what is important is that we know you are safe.
"However there may be other people who were in there on the night, but others may not have been aware were there".
He told reporters that the investigation's "absolute priority" is to establish the identities of those inside the building.
"We have colleagues in there as we speak, searching for and recovering those that have died".
"It may take longer than that".
"A priority of each and every one of us involved in the ongoing operation at Grenfell Tower is to recover and identify all the victims", he said.
"The reason we had to pause the search and recovery yesterday was for the safety of our staff". City police have announced 58 people remain missing and "we assume likely to have died". "But we need to make sure that that actually happens". "I absolutely get why they are angry".
"The investigation will be exhaustive. What we want is for someone from the public authority to tell us what the procedure is".
In a statement to mark the official celebration of her 91st birthday, she said: "It is hard to escape a very soreer national mood" after a "succession of terrific tragedies".
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