Hundreds of protesters took to the streets of London on Friday to demand answers over the catastrophic blaze that tore through the Grenfell Tower housing block in west London.
There were angry scenes at the offices of the Kensington and Chelsea council, which was responsible for managing the 1970s social housing block in a working-class enclave of one of Britain's richest areas.
Cundy said there may have been other people in the tower that police are not aware of, which would add to the final death toll.
Some 19 patients are still being treated in hospital, of whom 10 are in a critical condition, the National Health Service said Saturday. She said: "Frankly, the support on the ground for families who needed help or basic information in the initial hours after this appalling disaster was not good enough".
Speaking on Friday evening, Mrs May said: "Everyone affected by this tragedy needs reassurance that the Government is there for them at this bad time - and that is what I am determined to provide".
The Prime Minister came under fire as she visited victims of the tragedy and was heckled as she left.
Their teams were forced to leave the 24-storey building yesterday afternoon when the fire restarted, delaying further the efforts to reach upper floors - where many victims are thought to have been trapped.
In a television interview, she sidestepped questions over whether she had misread the public mood.
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It comes after police revealed that 58 people are missing and presumed dead. "Sadly, our work will be ongoing for many, many weeks.We know that there are still bodies of those who died inside the building and we want to return those people to their families as soon as we possibly can".
Earlier, a sign at a Tube station said that the service suspension was because of the "safety" of nearby Grenfell Tower, suggesting structural concerns.
A top former Conservative politician and Times of London columnist blasted May over her handling of the fire, and said that she must resign. "People have lost their lives, people have had their homes destroyed, they have fled for their lives with absolutely nothing".
Cundy said the police investigation would look into the building's 2016 refurbishment and promised to prosecute "if there is evidence".
"Grenfell is where they shove all the people who don't have any choice", said a resident as he watched his home burn. "United in our sadness, we are equally determined, without fear or favor, to support all those rebuilding lives so horribly affected by injury and loss".
"The prime minister is distraught about what has happened", said Green, who was appointed May's deputy in the wake of the general election.
There is simmering anger in the multi-ethnic Kensington area hit by the blaze, and public fury has been directed at senior government figures, including Prime Minister Theresa May, when they visited the stricken area.