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.
Cundy also said that the number of dead or missing in the fire has now risen to 79, but that number may change as the investigation continues, he said.
Grenfell Tower, a 24-storey apartment block in North Kensington, West London, was set up in 1974.
He said it had been "incredibly emotional working in there".
Rescue personnel have had difficulty reaching the top floors of the charred, 24-story tower.
Cundy explained that one of the reasons identification has been so hard is because dental records are needed from victims who hailed from different countries around the world.More news: Somalia blast kills at least 15, police say
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The investigation into the fire will span a "wide range of areas", Cundy said, from its original construction, to the refurbishment and how it has been managed and maintained.
Two British officials have said that new exterior cladding used in a renovation of Grenfell Tower may have been banned under United Kingdom building regulations.
Experts say the cladding and the insulation it contained seems to have spread the flames quickly along the exterior of the building, overwhelming safety devices like fire doors.
The Prince was photographed hugging a distraught woman who grieved for her husband, who went missing in the fire. "And therefore, sadly, I have to assume that they are dead", he said.
My understanding is that the cladding that was reported wasnt in accordance with United Kingdom building regulations, Hands told Sky News. The cops and the rescue department have intensified their search and service dogs have also joined the grim search for bodies in Grenfell Tower which turned into ashes.
May met with victims Saturday and promised millions of pounds in aid to help them get back on their feet.
Asked about this by the BBC's Andrew Marr, The Chancellor said: "My understanding is the cladding in question, this flammable cladding which is banned in Europe and the U.S., is also banned here".