Police Commander Stuart Cundy said the number of 58 is based on reports from the public and may rise.
He warned that a full forensic and systematic search will take weeks to complete, adding: "We must also prepare people for the bad reality that some people may not be identified due to the intensity of the fire".
May added that she will receive daily briefings from the stricken area, although it remains to be seen how much of the information will be made public.
Late Sunday, the Metropolitan Police released three photos from inside Grenfell Tower, which showed in close detail how the fire charred the 24-story building that once housed up to 600 people in 120 apartments.
"Those who mock health and safety, regulations and red tape need to take a hard look at the consequences of cutting these and ask themselves whether Grenfell Tower is a price worth paying".
King also said that there are around 4,000 tower blocks in the United Kingdom without automatic fire sprinkler protection systems in place.
Prime Minister Theresa May's government earlier sought to quell anger over the fire, pledging to support the victims of the blaze after protesters jeered her when she visited local residents.
The group, which spent two-and-a-half hours with May on Friday and Saturday, hit out at the "longstanding neglect" of council buildings in the area. More than 3 million pounds ($3.8 million) has been raised for the victims, and the British government has announced a 5 million-pound ($6.3 million) emergency fund.
The anger on the streets of London's North Kensington has been growing in the past 48 hours.
The identification of the victims is proving very hard - which experts attribute to the extreme heat of the fire.
Mr Cundy said: "The conditions due to the fire damage verge on indescribable, which is why this will be such a lengthy operation taking weeks to complete".
Officials are using dental records, fingerprints and DNA samples to try and positively identify victims.
A solemn Elizabeth and her husband Prince Philip held a minute of silence for the fire victims at the start of the procession Saturday.
She said in her message on Saturday: "Today is traditionally a day of celebration".
Hundreds have been left homeless by the blaze, putting more pressure on officials in a city plagued by a chronic housing shortage.
"It was a death trap, and they knew it", one person shouted as demonstrators surged inside the offices of the Kensington and Chelsea council, responsible for managing the social housing block in a working-class enclave of one of Britain's richest districts.
Corbyn has written an open letter to the Prime Minister, calling for the public inquiry to ensure "all necessary lessons are learned".
Engineering experts and fire safety specialists believe the building's exterior cladding may have quickly fuelled the blaze, overwhelming fire protection devices.
The tragedy has provoked a huge response from nearby communities.
Many survivors are sleeping on the floor in community centers and there's still no coordinated distribution of donated food and clothing.
He said: "Whilst our teams have been from the bottom to the top of the tower, we must now carry out a full forensic and systematic search".