Mrs May has promised a public inquiry into the catastrophe, and also pledged £5 million (Dh23.5m) of support, housing guarantees and help with access to bank accounts and cash.
Angry protesters chanting "We want justice" stormed their way into the Kensington and Chelsea town hall on Friday.
He says it will take weeks or longer to recover and identify all the dead in the public housing block that was devastated by a fire early Wednesday.
Questions too over whether local authority cuts and a lack of fire prevention measures contributed to the disaster.
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.
A short walk away, however, are apartments and houses that cost millions of pounds and are home to a wealthy elite that residents of the Grenfell Tower had seen as a world apart.
Police have said criminal prosecutors will be pursued if there is evidence of wrongdoing. "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. Cundy said emergency workers have now reached the top of the tower.
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.
Then there are the many people who have been left homeless leaving the local authority with the task of finding them suitable accommodation as a matter of urgency.
There have been demands for answers as to how the blaze was able to engulf the building, trapping many on the upper floors. The neighborhood's resident's association said the management company was negligent.
The fire broke out less than a week after a election in which May lost her parliamentary majority.
Earlier on Friday, May met victims privately at a central London hospital.
"The package of support I'm announcing today is to give the victims the immediate support they need to care for themselves and for loved ones", she said, according to the Downing Street statement on Friday. "They didn't. They left him".
One of her closest allies, Mr Damian Green, defended Mrs May yesterday.
But a clergyman who was present at the No 10 meeting said Mrs May showed empathy as she talked for two and half hours to survivors. While failing to answer, she said the focus was now on providing support to the victims. "You have to be prepared to receive people's emotions, and not be so frightened about people", former Conservative cabinet minister Michael Portillo told the BBC.
Sadiq Khan has joined a congregation at a church service near Grenfell Tower.
Queen Elizabeth II said the disaster had cast a sombre pall over Britain, but insisted the country was showing resolve in the face of adversity.
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