On Friday evening, May was interviewed by Emily Maitlis on the BBC programme "Newsnight" where she sidestepped questions over whether she misread the public mood and anger over the Grenfell fire as well as what her personal response is - leading to more criticism of being called "robotic" and "cold".
London has a chronic housing shortage even in the best of times, and those left homeless by the fire - already angry over what they see as government inequity and incompetence - fear being forced out of the British capital.
Detectives investigating the fire at Grenfell Tower in London say new footage of the gutted building's burned-out interior shows just how hard the task of finding and identifying bodies is proving to be.
Service on two London Underground lines has been partially suspended because of concerns about the safety of the high-rise in the fire that killed at least 30 people.More news: Trump lawyer denies president is a probe target
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After meeting with Grenfell survivors on Friday, Ms May announced a 5 million pound (AUS$8 million) fund to help them and expressed sorrow for their plight. The reason for that - at one point, in terms of our casualty bureau, there were 400 people who were reported missing from Grenfell Tower.
"We've always been advocates of automatic fire sprinkler protection in tall tower blocks and they work - people don't die in sprinkler buildings", he said.
"Within the community, trust in the authorities is falling through the floor and a suspicion of a cover-up is rising", said Lammy, who lost a close friend in the fire.
The fire at the 24-story building has led to community anger and protests over the British government's response. "My government will do whatever it takes to help those affected, get justice and keep our people safe", she said.
The government has promised a full public inquiry, but that has done little to a sense of frustration at the lack of information about how the fire moved so quickly to engulf the building.
He said a police investigation by specialist detectives would "establish the facts to provide, as best we possible, answers for those so deeply and tragically affected by the bad fire at Grenfell Tower".
The Grenfell Tower housed about 600 people in 120 apartments.