The latest update includes the 30 already confirmed to have died in the catastrophic fire in a west London tower block in the early hours of Wednesday morning.
New cladding on the building has since been named as a potential factor in the quick spread of the fire.
Police had earlier put the toll at 58 presumed dead.
Cundy promised an “exhaustive” criminal investigation into the fire that would also look at a major refurbishment of the building completed previous year.
Speaking to SkyNews on Sunday, Labour MP David Lammy said some contractors working on the Grenfell Tower were removing evidence of their work after the last week inferno that killed dozens of people in the 24-story building.
“And it is incredibly hard to describe the devastation in some parts of that building”, Cundy said. Cundy said he would be “looking at all criminal offenses that might have been committed by any individual or any organization”.
Trade Minister Greg Hands said the government is carrying out an “urgent inspection” of the roughly 2,500 similar tower blocks across Britain to assess their safety.
The remains of Grenfell Tower stand in London on Saturday.
By the blackened Grenfell Tower, firefighters took off their helmets and stood still to observe the minute’s silence, some with their arms around each other’s shoulders.
Mr Khan said the images of the 24-storey building being ravaged by fire “should be forever seared into our nation’s collective memory”.
But a spokeswoman for the Prime Minister said: “We don’t support proposals to seize private property”. The meeting is unlikely to quell complaints that May has been slow to reach out to victims, despite her announcement of a $6.4 million emergency fund to help the displaced families.
British health authorities will also provide long-term bereavement counselling for those who lost loved ones in the tragedy.