Experts believe the exterior cladding, which contained insulation, helped spread the flames quickly up the outside of the public housing tower on Wednesday.
Previously, the Metropolitan Police had confirmed 30 people had been killed in the inferno; the announcement Saturday almost doubles that number. Sixteen bodies have been taken to the mortuary including one person who died in hospital - the others have been recovered from the building. "So that 58 would include that 30", he said.
He also said: "I understand, I really do understand the fears of so many about not knowing the scale of the tragedy that is unfolding behind us".
Commander Stuart Cundy said the number may still increase.
Only five victims have been formally identified - and Cundy said that because of the fire's intensity and the devastation it caused, authorities may not be able to identify everybody who died. She also says she will receive daily reports from the stricken neighbourhood. He asked anyone who was in the tower and survived to contact police immediately.
Meanwhile, police and firefighters have now reached the top of the tower in their search.
British outlets said May struggled to offer support or leadership in the wake of the blaze, accusing her of lacking emotional intelligence and calling her "Maybot".
After she met with fire victims, volunteers and local leaders, British Prime Minister Theresa May said support for families following the fire was "not good enough".
May said after the meeting Saturday that there have been "huge frustrations" in the community as people tried to get information.
But she added that because victims had been subject to a "very intense fire" that will made some of the identification "very difficult". Some said they had never seen a building fire advance so quickly.
Officials are using dental records, fingerprints and DNA samples to try and positively identify victims.
This year, however, it is very hard to escape a very sombre national mood.
Hundreds have been left homeless by the blaze, putting more pressure on officials in a city plagued by a chronic housing shortage.
Angry protesters chanting "We want justice" stormed their way into the Kensington and Chelsea town hall on Friday.
He insisted the Government had acted on safety recommendations after an earlier fire in London in 2009, but it would wait for the public inquiry's findings before making any changes in regulation.
Fire safety experts believe that cladding put on the building's exterior during a renovation a year ago was less fire retardant, which may have fueled the blaze.
The tragedy has provoked a very big response from nearby communities that have donated food and shelter to the victims.
Many survivors are sleeping on the floor in community centers and there's still no coordinated distribution of donated food and clothing.
He added: "We know how to do this we did it after the riots". The UK government has already announced a full judge-led public inquiry in an attempt to learn lessons from the tragedy and implement any necessary fire measures in other residential towers blocks.