On Sunday Chancellor Philip Hammond said there would be an investigation to see if building rules had been violated in reference to the cladding which had swathed the building, allegedly to improve the view from nearby luxury flats, and may have accelerated the blaze. The paneling has been blamed for quickly spreading the flames.
Police Commander Stuart Cundy said the number of 58, which was based on reports from the public, may rise and includes the 30 deaths that have already been confirmed.
It's an increase from the previous number of 58.
Mr Cundy said the police investigation into the blaze would look at the building and its refurbishment in 2016 and vowed to prosecute people if there was evidence.
"We've worked tirelessly to establish how many people we believe were in Grenfell Tower on the night and at this point in time we are unable to say that they are safe or well", he said.
"It's hard to describe the devastation the fire has caused", Candy said.
He said a police investigation by specialist detectives would "establish the facts to provide, as best we possible, answers for those so deeply and tragically affected by the awful fire at Grenfell Tower".
Activists had been complaining about fire safety at the tower for several years, with fears intensifying after a renovation completed last year that included new exterior cladding.
He said there are 79 people "either dead or missing, and I sadly have to presume [they] are dead".
Khan described the fire as a "preventable accident that didn't need to happen", adding that the "tragedy we're seeing is a effect of the mistakes and neglect from politicians from the council and from the government".
Dozens of people have been reported missing since last Wednesday's early-morning blaze that struck while many who live in the building's 120 apartments were asleep.
The recovery operation had been paused amid concerns for the safety of emergency workers in the building, but has now resumed.
The Government has announced a minute's silence to remember those who lost their lives and all those affected by the fire at Grenfell Tower.
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.
Anger among residents has been mounting in recent days as information about the missing has been scant and efforts to find temporary housing have faltered.