The fire is believed to have started on the fourth floor of the 24 storey tower block in the early hours of Wednesday morning before spreading up the building via the cladding on the external walls.
There were angry scenes at the offices of the Kensington and Chelsea council, which was responsible for managing the 1970s social housing block in a working-class enclave of one of Britain's richest areas.
Outside, many people lit candles and added flowers to banks of bouquets piled against the church walls.
"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 emergency services expect to find no more survivors.
Anyone who has concerns about someone who they know may have been living, visiting or staying in Grenfell Towers, but has not yet been contacted by the police or not yet reported their concerns about a possible missing person should call the police Casualty Bureau on 0800 0961 233.
Mrs May was greeted with cries of "coward" and "shame on you" as she returned to the site of the devastating fire in west London on Friday.
The NSW Master Builders Association said the danger lies in imported products that do not meet safety requirements.
The queen said it was "difficult to escape a very somber mood" on what is normally a day of celebration.
"In recent months, the country has witnessed a succession of bad tragedies", the monarch said, referring to the fire and the recent terrorist attacks in Manchester and London.
"During recent visits in Manchester and London, I have been profoundly struck by the immediate inclination of people throughout the country to offer comfort and support to those in desperate need", the queen said in a statement. He said he was "heartbroken by the tragic fire and the appalling loss of life".
UK govt rushes staff for rehabilitation of London fire victims
The tragedy has provoked a huge response from nearby communities that have donated food and shelter to the victim. The government has said the country will observe a moment of silence at 11 a.m.
But besides the drive to help survivors, the sense of anger was palpable on the streets.
"The key question now is whether the overall design of the building's complete exterior was properly tested and subsequently signed off by the relevant authorities including the fire officer, building compliance officer and architect before commencement of the project".
Protesters marched to the edge of the police cordon around the tower, shouting "no justice, no peace", where a few young men tried unsuccessfully to break through.
The money will come from the £5 million fund announced by Mrs May on Friday. "As prime minister, I will be responsible for implementing its findings". One of them told reporters they spoken to the Prime Minister for two and a half hours about their demands and what they expected.
Commander Cundy further informed that the police investigation into the fire "will take weeks, it may take longer than that".
"My understanding is that the cladding that was reported wasn't in accordance with United Kingdom building regulations", Hands told Sky News.
The fire forced residents to flee through black smoke down the single stairwell, jump out of windows or even drop their children from the 120-apartment building.
Mohammed Alhajali has been the first victim identified from the fire.
After she met with fire victims, volunteers and local leaders, British Prime Minister Theresa May said support for families following the fire was "not good enough".
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