Demonstrators crowd a staircase at Kensington Town Hall, during a protest following the The Grenfell Tower fire.
Protesters demonstrated outside the church where PM made announcement.
Police broke up a scuffle between members of the crowd as the Mrs May's auto drove off. "We do not want another fatality arising out of this tragedy".
Firefighters are still searching for victims in the 24-story Grenfell Tower that went up in flames early Wednesday.
"The response of the emergency services, NHS [National Health Service] and the community has been heroic", May said in a statement released Saturday after the prime minister met with victims and community leaders.
"She should have been there with the residents".
"What I'm now absolutely focused on is ensuring that we get that support on the ground", May told the BBC.
London fire: Tower victims 'may never be identified'
Sidani Atmani, 41, made it to safety from the 15th floor, but only after trying to help a disabled man get down the stairs. Newham Council said it had carried out a fire risk assessment at Ferrier Point in March and no issues had been identified.
Residents of the tower say May was far too slow to visit the stricken community, that the building had been unsafe, and that officials have failed to give enough information and support to those who have lost relatives and their homes. The reason for that - at one point, in terms of our casualty bureau, there were 400 people who were reported missing from Grenfell Tower.
Tower residents and many others in the area are still struggling to come to terms with what they have seen and lived through.
"Unfortunately this had to happen for things to happen". And as NPR's Frank Langfitt in London, police are hoping that the death toll will not reach the triple digits.
"That's one of the most bad things I have ever seen", Prince William said of the tower's blackened shell.
"We as the police, we investigate criminal offences - I'm not sitting here and saying there are criminal offences that have been committed, that's why you do an investigation, to establish it".
The Syria Solidarity Campaign said Alhajali, a civil engineering student, had been in a flat on the 14th floor when the fire broke out, and had spent two hours on the phone to a friend in Syria.
Mr Cundy added that the figure could change. However, police have also said they do not expect to find any other survivors and that the number is likely to rise significantly.
Police have warned some of the victims may never be identified due to the state of the remains.