The fire, at broke out at the 24-storey block, which contained 120 one and two-bedroom flats, shortly before 01:00 BST on Wednesday.
It tore through all floors of the building and took more than 200 firefighters 24 hours to bring it under control.
Protests were held in London on Friday as residents demanded more support for those affected by the fire.
Between 50 and 60 people stormed Kensington and Chelsea Town Hall as members of the public said the homeless needed help "right now".
There were also angry scenes outside the Clement James Centre, in North Kensington.
Dozens of demonstrators surged towards the entrance and there were scuffles outside as organisers appealed for calm.
The BBC's Matthew Price said locals had told him they wanted the prime minister to "cut out" Kensington and Chelsea council from the relief effort.
He said senior members of the residents' association described an "absolute chaos" of "no organisation" from officials. He added: "They do not believe they are capable of managing the response. Such is the total and utter lack of trust."