Police have said it could take months to search the building and some victims might never be identified.
London Police has launched an investigation to determine whether any crimes contributed to the blaze.
Meanwhile, experts have said sprinklers could have been fitted in the tower for £200,000, but Nick Paget-Brown, the Tory leader of Kensington and Chelsea Council, said there was not a "collective view" among residents in favour of installing them.
The area surrounding the tower has been plastered by desperate relatives with pictures of the missing, from grandparents to young children. He said that 24 people were being treated in hospitals, including 12 in critical care.
The monarch has expressed her sympathies to families of victims of the blaze that ripped through the 24-story building, killing at least 17. The protesters were angered when no one from the council came out to address their concerns, reporters said.
Angry residents on Friday surrounded Andrea Leadsom, a Conservative Party lawmaker and leader of the House of Commons, when she visited the neighborhood, demanding to know why British Prime Minister Theresa May hadn't met with survivors when she toured the area a day earlier.
The paper also said that the last full assessment of fire risks for the building was in December 2015, before the refurbishment was completed a year ago.
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Two days after the fire broke out early Wednesday in the local authority-owned apartment block, firefighters were yet to access some of the floors due to worries about the stability of the structure.
Queen Elizabeth II and Prince William made an emotional visit on Friday to see the survivors, victims' families and rescue workers who were affected by the deadly fire at Grenfell Tower in London. While the cause of the blaze has not been officially identified, residents had been complaining about conditions in the building since it was remodeled in 2016, but were rebuffed.
Ms Alia Al-Ghabbani, a receptionist who lives in the estate, was among many angered by a recent refurbishment in which new cladding was added to the exterior of the building and which media reports said might have played a part in the rapid spread of the fire.
The group previous year completed a 10 million pound ($12.8 million) renovation that included new outside insulating panels, double-paned windows and a communal heating system.
Housing Minister Alok Sharma said the government "stands ready to provide every assistance - we will support every family that is affected".
"We as the police, we investigate criminal offences - I am not sitting here and saying there are criminal offences that have been committed, that's why you do an investigation, to establish it", he said.
The 39-year-old, who has lived in the block for 20 years, said: "I let the bathroom flood".
"I am today ordering a full public inquiry into this disaster".