"I have stressed to the task-force the need for local residents and the wider public to be provided with as much information as possible and for there to be maximum transparency".
They demanded justice for the victims and claimed Wednesday's fatal blaze was due to negligence, with many citing the new cladding put on the 1974 concrete tower.
Families of the victims and residents of Grenfell said they were furious that the local government had for years ignored their complaints about the building's lack of measures in case of fire and had not adequately attended to survivors of the blaze.
The area surrounding the tower has been plastered by distraught relatives with pictures of the missing, from grandparents to young children.
At least 58 people are dead or presumed dead after the blaze.
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.
Dozens of police officers held back booing crowds and broke up scuffles as her auto drove off from a local church, where she had met survivors, residents and volunteers and promised new funds for those affected.
As the victims of the fire entered the Downing Street, hundreds of demonstrators had gathered in Whitehall to protest against the prime minister. "As Prime Minister, I will be responsible for implementing its findings".
"But, frankly, the support on the ground for families who needed help or basic information in the initial hours after this appalling disaster was not good enough".
The fire has also been transformed into a symbol of class inequality - the Grenfell Tower's charred remains stand high above one of the British capital's wealthiest neighborhoods.More news: Play ball! GOP, Democrats battle as one - Team Scalise
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He told the Press Association: "I'm positive because I think it was a real chance for local residents, people affected by this tragedy, to voice their concerns directly to the Prime Minister so that she could hear them".
She also pledged 5 million pounds ($6.39 million) of support, housing guarantees and help with access to bank accounts and cash.
"It will go to establish the answers of what happened in the fire and how it spread; it will look at the building itself; it will look at the refurbishment as well".
"Both myself and colleagues from London Fire Brigade have already said it will take weeks".
Some 19 patients are still being treated in hospital, of whom 10 are in a critical condition, the National Health Service said Saturday.
She will meet victims, volunteers and community leaders afterwards, said Downing Street.
After a turbulent three months which has seen three militant attacks and now the tower blaze, Queen Elizabeth said "it is hard to escape a very sombre national mood", in a message on her official birthday.
In a message released on her official birthday, the Queen said it was "difficult to escape a very sombre mood", following recent attacks and deaths in London and Manchester.
"Nowadays, we would not dream of building towers to the standards of the 1970s, but their inhabitants still have to live with that legacy".
"Mohammad was a very incredible and kind person".