When the building was refurbished, "there were so many worries", Labour councilor Judith Blakeman, who liaised with the building's residents, told the BBC on Friday.
He said: "What did she bring, what useful things did she bring?"
Mr Khan was heckled by angry crowds as he visited Grenfell Tower, including a seven-year-old boy who asked: "How many children died?"
He added: 'For those of us that have been down there, it's pretty emotional, so I hope it is not triple figures'. "This is our town".
As others shouted for legislation requiring that Britain's aging public high-rises be retrofitted with sprinkler systems and multiple stairwells - which were lacking at Grenfell Tower - Khan said he shared their frustration and called for the government inquiry into the blaze to publish its initial findings by the end of the summer.
"I have friends in the tower and they are not telling us anything", Salwa Buamani, 25, told AFP.
"My block went up on Wednesday so what Theresa May are you doing here on Friday? I lost my home on Tuesday, people lost their lives on Tuesday".
The announcement comes after Mrs May was branded a "coward" as she left St Clement's church in Kensington followed by a furious crowd. They're also angry that the emergency services have been taking so long to identify who these victims are.
The list includes immediate re-housing of all the victims of Grenfell Tower fire within the borough, immediate release of funds to cover costs of welfare and all losses suffered by the victims, and launching an investigation into the recent refurbishment project of the tower.
Earlier, in a statement, she said: "The individual stories I heard this morning at Chelsea and Westminster Hospital were horrific".
Queen Elizabeth II, in a message released on her official birthday on Saturday, said the United Kingdom has been "resolute in the face of adversity" following recent tragedies in London and Manchester.
Some desperate residents pleaded to speak to the queen and her grandson about their plight and the fate of missing children as they left the site, with William promising he would return. It was one of many government-owned buildings that was remodeled under an urban regeneration plan in order to increase the number of units, while making it more appealing to private tenants. Take a look at Ireland's first social chat show - featuring live studio guests John Connors and Mark O'Connor of new smash Irish movie, Cardboard Gangsters; Matthew McConaughey sits down with Niall Horan, there's music from The City And Us, crackin" new comedy from Shifts and Joe Gorman is taught the ways of the farm by the legendary John "The Bull' Hayes.
"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".
Hundreds of people marched from Kensington town hall toward the gutted tower on Friday evening, some brandishing Socialist Worker Party placards emblazoned with slogans including "Defy Tory Rule" and "no justice, no peace" and 'the rich, the rich, we've got to get the rich'.
His request was followed by chants of "we want justice".
Police barred their way and scuffles broke out.
While the deadly blaze at the Grenfell Tower in north Kensington has prompted an outpouring of generosity, it has also unleashed rage at the authorities as the charred tower was cast as a deadly symbol of a divided society. 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.