She declined to speak to anyone outside the meeting where an angry crowd had gathered and police broke up a scuffle among the group as Mrs May's auto drove off.
Demonstrators pushed their way through an automatic door shouting 'We want justice!' and 'Killers!' as they clashed with security guards in the lobby. The residence is believed to have had as many as 600 people inside it when the fire broke out on one of the lower floors.
They met volunteers, local residents and community representatives while visiting Westway Sports Centre in west London, near the burnt down 24-storey Grenfell Tower.
May has faced criticism for not meeting with survivors during her first visit to the site after the blaze, the wire service reports.
While the disaster has prompted an outpouring of generosity, there was also fury at the authorities as the charred tower was cast as a deadly symbol of a divided society.
Metropolitan Police commander Stuart Cundy responded to speculation that the number of dead could exceed 100, saying: "For those of us that have been down there, it's pretty emotional, so I hope it is not triple figures, but I can't be drawn on the numbers". The monarch has expressed her sympathies to families of victims of the blaze.
The package includes a guarantee to rehouse people as close as possible to where they previously lived - a poor neighbourhood surrounded by extreme wealth.
The death toll from the London fire stands at 30, and is still climbing.
Local residents have accused police of hiding the true toll.
"So it is right that in addition to the immediate fire report that will be produced and any potential police investigation, we do have a full public inquiry to get to the bottom of this".
He also said survivors from the tower would be re-housed in the local area.
"She wanted an entirely controlled situation in which she didn't use her humanity", former cabinet minister Michael Portillo told the BBC.
Portillo said: "The Prime Minister would have been shouted at by the residents, but she should have been willing to take that".
- Boris Johnson has accused Labour of "outrageous politicking" over the fire. He said that number was expected to rise.
"That's one of the most bad things I have ever seen", Prince William said of the tower's blackened shell. One Moroccan woman in the mosque, Habiba, said she was looking for a 16-year-old Moroccan school girl Nur Huda El Wahabi who is missing, who is best friends with her son Abdul.
Meanwhile, the police have said that some of the dead, from the devastating blaze may never be identified, as officers warned that the painful process of retrieving the victims could take months.