Britain held a moment of silence for the victims on Monday, with emergency service workers bowing their heads in respect.
Engineering experts and fire safety specialists believe the building's exterior cladding may have quickly fueled the blaze, overwhelming fire protection devices.
Commander Stuart Cundy said he expects the ongoing search and recovery effort to last "many, many weeks", as authorities work to identify the victims.
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Previously, the Metropolitan Police had confirmed 30 people had been killed in the inferno; the announcement Saturday almost doubles that number.
"It will also be a subject that the separate criminal investigation will be looking at", he said.
Cundy said the search and recovery operation was ongoing in the burnt-out 24-storey tower, which was built in 1974 and had received a major refurbishment that was completed past year.
"Within the community, trust in the authorities is falling through the floor and a suspicion of a cover-up is rising", said Lammy, who lost a close friend in the fire.
Portugal's deadliest fire kills 62 while fleeing the blaze
Every few miles, I passed burned-out carcasses of cars on the side of the road. "I am complete stunned by the number of deaths". Portuguese President Marcelo Rebelo de Sousa flew overnight to the scene and spoke on arrival of an "unprecedented situation".
UK Prime Minister Theresa May has admitted that support for victims of Wednesday's deadly Grenfell Tower fire in London was "not good enough". "Are there other tower blocks across London and across the country that have that cladding?"
Speculation has focused on the role that cladding apparently used in a recent refurbishment of the tower may have played in the fire.
Many in the United Kingdom are upset with Prime Minister Theresa May for her response - or lack thereof - to the Grenfell Tower fire.
An additonal 70 people are reportedly missing.
At a daily briefing with reporters, Mrs May's spokeswoman said the terms of reference of a public inquiry into the tower blaze were being drafted. "It's really hard to describe the devastation the fire has caused". "And it can be very time consuming, but my absolute commitment to all the families and the loved ones of those that died is that we will do this as quickly as possible".
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