One woman wept, saying it was because the PM declined to speak to anyone outside the meeting which lasted less than hour.
On Saturday afternoon, hundreds of protesters gathered in Whitehall to call for her resignation. He said there are roughly 2,500 similar apartment towers throughout Britain.
So far, 58 people have been feared dead - a toll that authorities warn could rise ahead of new figures to be released on Monday. All the rest are homeless.
The tragedy has provoked a huge response from nearby communities.
Following the meeting, May issued in a statement in which she acknowledged that "support on the ground for families that needed help or basic information in the initial hours after this appalling disaster was not good enough".
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.
He said it will take "weeks or longer" to recover and identify all the dead in the social housing building that was left charred and gutted by the devastating blaze.
Cundy said a full forensic and systematic search was being carried out, but people must prepare for the worst.
The British police fired a stun gun at a man who reached for a knife as he ran towards officers at one of the gates to the Westminster parliament in central London yesterday, witnesses said.
Their investigation into the fire would "establish the facts and provide answers" as to the cause of the fire, Cundy said. He says "my heart goes out to those affected".
But a report by the Royal Borough of Kensington and Chelsea's Director of Housing just 11 months ago said the tower's safety credentials were exemplary.More news: Trump Times: Make America (nyet) Russia Great Again! (Washington Diary)
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Major roads near the stricken building were open Saturday. "I have heard the concerns and I have ordered immediate action across the board to help victims' relatives and the survivors", she said. People have lost their lives and others have lost everything.
May is chairing a government task force on the fire and a spokesman says that she will meet afterward with "a group of residents, victims, volunteers and community leaders" at No. 10 Downing Street.
Of the 58, he said the number of confirmed fatalities in Wednesday's inferno remains at 30.
"Put to the test, the United Kingdom has been resolute in the face of adversity", she added. At least 58 people are believed to have died in the blaze.
The leader of Britain's main opposition party is calling for the government to take over empty homes for use by residents displaced by the London high-rise fire.
On Saturday, NHS England said 19 people were being treated in hospital, including 10 in critical care.
The fire at the 24-story building has led to community anger and protests over the British government's response.
May has announced a fast-tracked public inquiry into the fire and said every household affected by the blaze would receive a minimum payment of £5,500 pounds from a £5 million emergency fund.