Police also identified the first known victim of the fire, 23-year-old Mohammed Al-Habjali, who lived in Grenfell Tower.
Queen Elizabeth II said the disaster had cast a sombre pall over Britain, but insisted the country was showing resolve in the face of adversity.
But she sidestepped questions over whether she had failed to judge the public mood.
He added: "They do not believe they are capable of managing the response".
Cundy said police will investigate the tower's refurbishment project, which experts believe may have left the building more vulnerable to a catastrophic blaze.
Fifty-eight people who were in Grenfell Tower are still missing and are presumed to be dead, London police announced Saturday, raising the death toll in the horrific inferno that turned the public housing block into a charred hulk.
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The area surrounding the tower has been plastered by distraught relatives with pictures of the missing, from grandparents to young children.
If the number is confirmed, it would make the Grenfell Tower blaze the deadliest in London since World War Two.
British Prime Minister Theresa met the families of the victims on Saturday and assured them a total compensation of $6.4 million for emergency costs and for finding homes in nearby locations within three weeks, according to Bloomberg.
In this photo released by the Metropolitan Police on Sunday, June 18, 2017, a firefighter stands outside of the Grenfell Tower after fire engulfed the 24-storey building, in London.
Investigators are now trying to establish the cause of the fire and how it spread so quickly through the block.
Following the meeting, a spokesman for the group of residents said he had given the PM their demands and a statement would be made to the community.
May chaired a government task force on the disaster before meeting survivors.
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Only a few days ago we hosted a Great Get Together in memory of Jo Cox, attended by people of every faith and background". He said: "The attack unfolded whilst a man was receiving first aid from the public at the scene; sadly, he has died".
May was rushed away from a meeting with residents on Friday under heavy police guard as protesters shouted "Shame on you" and hundreds stormed a local town hall calling for justice.
Former Conservative minister Michael Portillo said on Thursday that, although she had met in private with members of the emergency services, she should have met Grenfell Tower residents, as Labour leader Jeremy Corbyn did.
Pressed again on whether she had failed to understand the anger felt by the public, she said: "This was a bad tragedy that took place".
"It is hard to escape a very sombre national mood", the queen said in a statement to mark her official birthday - an occasion that typically does not result in any public comments from the monarch.
The fire ripped through the high-rise early Wednesday.
Saturday's newspapers conveyed the sense of anger on the streets. "This is an absolutely bad fire that took place", May said.
The Daily Telegraph claimed left-wing militants had been hijacking the demonstrations and deliberately spreading political fake news conspiracy theories about the blaze.
London fire: Death toll climbs to 79
He says it may be necessary for numerous outmoded tower blocks built in the 1970s to be demolished because of safety concerns. A resident in a nearby building watches smoke rise from a building on fire in London , Wednesday, June 14, 2017.
First Secretary of State Damian Green, May's deputy, told BBC radio that the inquiry would have interim reports and "we want the response to be as fast as possible".
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