Local residents shouted angry questions when London mayor Sadiq Khan paid a visit to the area.
Protesters gathered to call for help for the residents of the burned building, and the BBC reports that dozens of people "stormed Kensington and Chelsea Town Hall with a list of demands".
More than 70 people are unaccounted for, according to media reports, although it was not known whether some of those were among the bodies recovered so far.
NHS England says the injured are being treated in four London hospitals. Of those, 10 remain in critical condition.
Previously, the monarch had released an unprecedented statement in which she said that the United Kingdom remained "resolute in the face of adversity", in reference to the terror attacks in Manchester and London, as well as the deadly fire.
The 91-year-old monarch said it is "difficult to escape a very sombre mood" on what is normally a day of celebration.
No further survivors are expected to be found and criticism continues to mount for Prime Minister Theresa May's response to the tragedy.
The upper floors of Grenfell Tower sustained significant damage, he says, and "the sad reality is that this work will take some time, stretching into many, many weeks". Hundreds have been left homeless by the blaze, putting more pressure on officials in a city plagued by a chronic housing shortage.
London police said an investigation, led by a detective from its homicide and major crime unit, would examine whether criminal offences had been committed although they said there was nothing to suggest the fire was started deliberately.
Relatives of those missing after a high-rise tower blaze in London posted pictures of their loved ones Friday in the desperate hope of news, as grief following the tragedy has turned to outrage at authorities accused of being lax in meeting building standards. British officials have ordered a review of other buildings that have had similar renovations.
As of Friday morning, the death toll had risen to 30. Friday, some heckled May and chanted "coward" as she made her address at London's St.
The tragedy has provoked a big response from nearby communities that have donated food and shelter to the victims. May said the government would spend £5 million for clothes, food and emergency supplies to the victims. Wherever we can, we will bring people to justice if there is evidence. Corporate manslaughter. They were warned by the residents that there was an obvious risk of catastrophe.
Speaking on Friday evening, Mrs May said: "Everyone affected by this tragedy needs reassurance that the Government is there for them at this bad time - and that is what I am determined to provide".
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