This figure includes the 30 people already assumed to have lost their lives in the west London tragedy, though the number of those killed may rise still further.
Scotland Yard said 16 people have been recovered to the mortuary so far.
“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 they are dead,” Commander Stuart Cundy told reporters in west London on Saturday.
“The fire has been truly horrific, and for me this is just a human tragedy,” Commander Cundy added.
“Yesterday afternoon, following expert advice... we had to pause that search and recovery. I am pleased to say that as of this afternoon, we are now back in Grenfell Tower.
“We’ve worked tirelessly to deal with the huge number of calls to our casualty bureau. Over 6,000 calls have been received into centres up and down the United Kingdom.
“We’ve worked tirelessly to determine the number of people who were in Grenfell Tower on the night and that at this point in time we are unable to say whether they are safe or well.”
Commander Cundy said 52 families were being supported by liaison officers.
The number 58 may change, he added. “There may be other people who were in there on the night, that others were not aware,” he said.
He “came to the UK because he had ambitions and aims for his life and for his family,” they added.
And addressing criticism of the response to the disaster, Prime Minister Theresa May said support for families “who needed help or basic information in the initial hours” after the event “was not good enough”.
The Philippine Embassy of the UK is appealing for information about Ligaya Moore, 79, who lived on the 21st floor
Maria Del Pilar Burton, 65
Maria Del Pilar Burton, 65, and her husband Nicholas were caught up in the blaze. Nicholas has regained consciousness and has appealed for help to trace his wife. He is certain she got out of the building. Maria has Alzheimer’s.
Nadia Choucair, 33
The teaching assistant was in a flat on an upper floor with her husband Bassam, and three daughters, aged 3, 10 and 13. Nadia's mouther Sirria is also missing.
Stevan Racz shared a picture of his uncle Dennis Murphy, saying he called his family saying he was trapped on the 14th floor during the blaze.
Raymond ‘Moses’ Bernard, 65
Kritchanut via Getty Images
A family friend confirmed to the Press Association that Raymond Bernard, 65, known to his friends as Moses, is missing.
He had lived in Grenfell Tower since at least 2003. A 53-year-old woman called Karen Bernard is also registered to the same apartment.
Abdul Hanif, 26 (pictured), Abdul Hamid, 29 and Kamru Miah, 82
Abdul Hanif is pictured here with his sister Husna Begum, whose body and that of their mother have been recovered from Grenfell Tower. The three male relatives remain missing.
Ernie Vital, 43
Ernie Vital, from the Dominican Republic, lived on the 16th floor for more than 20 years. Majorie Vital, 68, (left) has been identified as having lost her life in the fire.
Lucas James, 12
Kritchanut via Getty Images
A 16-year-old girl told the Telegraph she feared her younger brother may have been staying with a friend on the 17th floor of the block.
The teenager, who lived with her mother on the eight floor, said: “We cannot find him, we have been going around hospitals.”
Steven Power, 63
Rania Ibrham, 30
Facebook/ Rania Ibrham
The mother-of-two sent a message to a friend begging for help but neither she nor her children aged five and three have been seen since the blaze.
A Facebook Live video was posted on her account that revealed her fearfully venturing into the hallway and urging other residents to come into her apartment for safety. She can be heard murmuring frantic prayers throughout and is heard to say (in Arabic): “There’s fire and smoke from beneath and above. See all the smoke above us.”
Ibrham, whose position on her Facebook page is listed as executive director at a Saudi Arabian charity, can be heard uttering reassurances to her family but also asking how they are supposed to get out of the building.
Mariem Elgwahry, 27
Mariem Elgwahry, 27, was on the 19th floor of the building and has been missing since news of the blaze broke. Her mother, Suhar, is also unaccounted for.
Briti Habtom, 35 and her son Briuk, 12
Mohamed ‘Saber’ Neda, 57
Neda’s family say he urged his wife Shakila, 45 and son Farhad, 24, to flee the blaze, but was unable to join them because he was injured. He was last seen on the stairwell injured and helping neighbours. He and his family lived in a top floor flat.
Hesham Rahman, 57
Twitter user Noha posted a picture of her brother, adding he was living in a 20th floor flat. “He is still missing, please share,” she asked.