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.
London Fire Brigade warns Grenfell Tower inferno investigation could take YEARS
The measures were announced following the second meeting of the Grenfell Tower Recovery Taskforce, chaired by the Prime Minister. Fifty-eight people are confirmed or presumed dead in the fire and authorities fear that death toll will rise.
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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Forty-two Israelis have been killed in knife, gun and car-ramming attacks by Palestinians or Israeli Arabs since October 2015. Israel had eased restrictions on the entry of Palestinians to Jerusalem and Israel from the West Bank for Ramadan.
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.
Kenya Moore from 'RHOA' got secretly married, BTW
She was everything to me. "Since we reconnected you have been my everything, my one and only, my heart.I love you", she wrote . News that the 46-year-old reality star has been intentionally "keeping her boo on the low for a minute now".
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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