Told there was a need for the public to hear her say something had gone badly wrong and the Government accepted responsibility, Mrs May said: "Something awful has happened".
While the blaze has prompted an outpouring of generosity, with many people donating provisions and clothes, it has also unleashed rage at the authorities as the charred tower was cast as a deadly symbol of a deeply divided society.
"At least she could've met the victims, [Labour leader Jeremy] Corbyn was a good man. he came and met the people", one victim told Sky News.
Scuffles broke out near the Kensington and Chelsea town hall offices on Friday as demonstrators chanting "We want justice!" surged toward the doors.
It issued a statement before the protest to try to address the concerns of residents.
"We must also prepare people for the awful reality that some people may not be identified due to the intensity of the fire".
The Grenfell Tower fire was a "preventable accident" caused by "years of neglect" by the local council and successive governments, Mayor of LondonSadiq Khan said yesterday. "Kensington is one of the richest areas, how did they allow this negligence?"
A firefighter who battled an intense blaze devouring a 24-storey apartment building in London has been left wishing he did more.
The residents group said while it welcomed the funding it had not been consulted before the announcement was made.
May met victims privately at a central London hospital on Friday and had expressed her sorrow on television on Thursday after meeting emergency services personnel.
"I called him and said: "Where are you?', I said: 'Where are you?' He said: 'I'm in the flat.' I said: 'Why you didn't come?"