Earlier, dozens of people stormed the town hall building in the London's Kensington district where the tragedy was being discussed.
The Guardian newspaper reported that contractors installed a cheaper, less flame-resistant type of panelling in the renovation that ended in May 2016.
"The conditions due to the fire damage verge on indescribable, which is why this will be such a lengthy operation taking weeks to complete", Police Commander Stuart Cundysaid. "The bodies have been taken to a morgue, but more bodies remain in the building".
"I have friends in the tower and they are not telling us anything", said Salwa Buamani, 25, who came with her three-year-old niece on her shoulders.
Police said Saturday that their investigation would look at the building and its 2016 refurbishment, and vowed to bring prosecutions "if there is evidence". "He didn't come with a bunch of police.no one even saw her".
At least 58 people may have died in the massive fire that engulfed a 24-storey residential tower housing over 100 families in west London, Scotland Yard said on Saturday, warning that the casualty figures "may increase". He asked anyone who was in the tower and survived to contact police immediately.
The government is carrying out an "urgent inspection" of roughly 2,500 similar tower blocks across the country to assess their safety.
He said the group had spoken about their "demands and what we expect".
The meeting is unlikely to quell complaints that May has been slow to reach out to fire survivors, despite her announcement of a $6.4 million emergency fund to help the displaced families.
West London film producer Nisha Parti, who has been helping victims in Kensington, said the cash is being given to those checking into hotels in the wake of Wednesday's blaze. However, the identification of the other victims is proving very hard - which experts attribute to the extreme heat of the fire.
He said: "The investigation is a police investigation". Officials are using dental records, fingerprints and DNA samples to try to positively identify the victims.
The Government has also announced that a minute's silence will be held for the victims at 11am tomorrow.
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. In her traditional birthday message, the 91-year-old monarch made a reference to the "succession of awful tragedies", a day after she paid a visit to people affected by the massive Grenfell Tower blaze in west London.
In an interview, she was questioned over whether there was a need for the United Kingdom government to accept some responsibility for what had happened.
Khan, who grew up in public housing, said locals are still angry at the "poor response" from the local and federal government both before and after the tragedy - echoing an angry op-ed he wrote for The Guardian Sunday.
"We want it to be able to have interim reports as well", he added.
The British government Sunday scrambled to contain political fallout from the London high-rise inferno that has claimed at least 58 lives as officials focused on building materials that may have spread the fire quickly.
Building officials have not commented since the fire.
The tragedy has provoked a enormous response from nearby communities that have donated food and shelter to the victims. More than three million pounds ($3.8m) have been raised for the affected families.
Many survivors are sleeping on the floor in community centers and there's still no coordinated distribution of donated food and clothing. "What we are doing is putting in place the support that will help them", she added.
Some residents had warned months ago that the tower represented a unsafe fire risk.
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Flowers and missing persons posters were taped to the gates of the church, while bags of donations were piled outside the door. An additional public inquiry set up by the government will determine if building regulations had been broken.
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