One woman wept, saying it was because the PM declined to speak to anyone outside the meeting which lasted less than hour. He said there are roughly 2,500 similar apartment towers throughout Britain. All the rest are homeless.
The Prime Minister also set out to reassure victims about the upcoming judge-led public inquiry into the fire.
British officials say they are helping the Syrian family of the first officially confirmed victim of the London tower blaze to come to Britain.
After visiting Manchester and London after attacks or disasters, she said: "I have been profoundly struck by the immediate inclination of people throughout the country to offer comfort and support for those in desperate need".
Cundy said the images and video of the scenes inside the Grenfell Tower would be released on Sunday, adding "We will not do that until we have contacted all the families we are supporting to let them know that's our intention". Their search for missing residents has been stalled because of safety concerns over the tower's condition. He says "my heart goes out to those affected". "It may well be the defining outcome of this tragedy that the worst mistakes of the 1960s and 1970s are systematically torn down", he said.
The Grenfell Tower in west London, built in the 1970s and renovated several times, contains 120 homes.
A resident in a nearby building watches smoke rise from a building on fire in London, Wednesday, June 14, 2017.
Major roads near the stricken building were open Saturday. "How did they allow this tragedy to happen when it could have easily been avoided?" Grief over a high-rise tower blaze that killed dozens of p. There has been growing public anger at the government's initial response to the disaster's aftermath and reports that external paneling put up during a recent renovation contributed to the flames' rapid spread.
A representative of the families who met with May and spoke to reporters briefly after leaving 10th Downing Street said "we will be making this in the community, with the community".
They also made an appearance on the steps of Buckingham Palace for during the annual Trooping the Color Procession, a ceremony held in celebration of the Queen's birthday.More news: London police: 58 people assumed dead in Grenfell Tower fire
Tory MP Sarah Wollaston said she was "beyond disgusted" by the revelation. British health authorities say that 19 patients are still being treated at four London hospitals.
The prime minister was pictured through a long lens camera being briefed by senior figures of the emergency services visiting the site but not meeting any of the residents.
The cause of Wednesday's blaze in London is still under investigation, but anger has mounted in the community amid reports that exterior panelling used in an extensive renovation completed previous year may have helped the flames to spread.
Londoners and others have also donated huge amounts of food, water and clothing, and shelter, to survivors. More than three million pounds ($3.8m) have been raised for the affected families.
Mohammed, whose apartment is opposite the tower, had friends who lived in Grenfell's upper stories.
Anger over the causes of the fire and the government's handling of the tragedy have grown during the week.
Many are demanding answers for how the blaze spread so quickly.
More than 70 people are unaccounted for, according to media reports, although it was not known whether some of those were among the bodies recovered so far.
The 91-year-old monarch said it is "difficult to escape a very somber mood" on what is normally a day of celebration.
Labour Party lawmaker David Lammy said the Government and the police should immediately seize all documents relating to the building's renovation to prevent the destruction of evidence that could show criminal wrongdoing.