Rescue personnel have had difficulty reaching the top floors of the charred, 24-story tower.
At least 30 people were killed in the blaze and dozens more are still missing.
"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", a police spokesman told reporters.
"There is a risk we may not be able to identify everybody".More news: Wonder Woman breaks United States box office record for film by female director
The aluminium cladding, called Reynobond, was made by United States company Arconic and had a polyethylene core, which the reports said was slightly cheaper than fire-resistant models by the same manufacturer. "The bodies have been taken to a morgue, but more bodies remain in the building".
Residents and neighbours are demanding answers for how the blaze spread so quickly after reports said contractors installed a cheaper, less flame-resistant type of exterior paneling in a renovation of Grenfell Tower that ended in May 2016.
Prime Minister Theresa May, who ordered a public inquiry into the disaster, was criticized on Thursday for visiting the scene of the fire, but talking to officials rather than victims or survivors.More news: Andy Murray wary of Karen Khachanov test
A criminal investigation led by a senior detective from Scotland Yard's homicide and major crime command is under way with calls for "corporate manslaughter" arrests to be made.
Queen Elizabeth II, accompanied by grandson Prince William, paid a visit to the Grenfell Tower this morning where the number of missing is estimated to be around 76. "What are you going to do about it?" a young boy asked as Mr Khan tried to stop tensions rising further.
Rydon, the firm responsible for the overall refurbishment of the tower, said its work had "met all required building regulations - as well as fire regulations and health and safety standards".
May met with hospitalized survivors Friday after coming under criticism for failing to meet with angry residents of the building earlier in the week.More news: Leo Varadkar becomes Ireland's first openly gay Prime Minister-elect
The first victim to be formally identified was Mohammed Alhajali, a 23-year-old Syrian refugee, who came to Britain in 2014 with his brother. More than 3 million pounds ($3.8 million) have been raised for the victims, and the British government has announced a 5 million-pound ($6.3 million) emergency fund.
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