The blaze occurred early Wednesday and later engulfed all floors above the second in the 24-story building that contained about 120 apartments in north Kensington.
"I believe there may be people who were in Grenfell Tower that people may not know were missing and may not have realised they were in there on the night".
"But being with colleagues from the London Fire Brigade when I was in there, colleagues from the London Ambulance Service and other police officers, I think it's fair to say it is incredibly emotional working in there".
A minute's silence was held across Britain at 1000 GMT to honour the victims of the fire - a painfully familiar ritual after the country has been hit by three deadly attacks by militants in London and Manchester since March.
Only five victims have been formally identified - and Cundy said that because of the fire's intensity and the devastation it caused, authorities may not be able to identify everybody who died.
The fire has also been transformed into a symbol of class inequality - the Grenfell Tower's charred remains stand high above one of the British capital's wealthiest neighborhoods. During the visit, they met with first responders from the Emergency Services, as well as local residents and community representatives.
"That's why she totally accepted that it (the government response) hadn't been good enough".
"I have heard the concerns and I have ordered immediate action across the board to help victims' relatives and the survivors", she said.
Labour leader Jeremy Corbyn has already called on the government to conduct an investigation into reports that Gavin Barwell, the former housing minister who was recently appointed as the Prime Minister's adviser, had failed to OK a fire safety review request he had received. "It is our fault, '" Emily Maitlis said to May in an interview. There is ample food and water, but very little privacy or proper bedding, and with the tower destroyed, no one knows where they will be relocated or for how long. The fire has led to national soul-searching about inequalities and neglect of the poor.
Mr Cundy added: "Sadly that work leads me to believe that the number of people missing, but as yet unaccounted for has risen from yesterday's figure of 58".
He reiterated there is a police investigation underway and that it will look at how the fire spread.
Cundy said there may have been people in the tower that police are not aware of, which would add to the death toll.
At least 58 people are dead or presumed dead after the blaze.