"People have given money to the Kensington appeal in the expectation that that would be used rapidly to give direct help", she said, adding: "To hear that people are being given just £10 - I am just appalled to hear that".
Police say at least 58 people are either confirmed or presumed dead, with the figure likely to rise in coming days.
The interior of the 24-storey tower block was gutted beyond recognition, with police commander Stuart Cundy referring to the conditions as "indescribable". He asked anyone who was in the tower and survived to contact police immediately. Police and fire experts have said the fire was so intense that the process of identifying human remains will take weeks, if not months - and some victims may never be found. "It should define the leadership of May and she should be forced to resign", he said.
Cmdr Cundy says the new number may change as investigation continues.
During Mrs May's visit, it was announced a £5m (€5.7m) fund would be made available to pay for emergency supplies, food, clothes and other costs.
Only five victims have been formally identified - and Cundy said that because of the fire's intensity and the devastation it caused, authorities may not be able to identify everybody who died. There has also been a public outcry at the government's initial failure to provide up-to-the minute information.
The 91-year-old monarch said it is "difficult to escape a very somber mood" on what is normally a day of celebration.
"It is hard to escape a very somber 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. In recent years, London's skyrocketing home prices and housing shortage have left residents struggling.
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". He also explained that the figure was based on reports from the public and feared it might go up.
The tragedy has provoked a enormous response from nearby communities that have donated food and shelter to the victims. More than 3 million pounds ($3.8 million) have been raised for the victims.
Numerous displaced are living in churches and community centers.
Two Underground lines near the fire area were partially shut down on Saturday to make sure that debris did not land on the tracks.
"In the wake of (the) Grenfell fire we have to recognise that something has gone badly, badly wrong in this country, that predominantly poor people die in a towering inferno because possibly in the long term (there had been a) lack of public investment", Corbyn told ITV's Peston on Sunday programme.