Four more people whose bodies have been recovered were identified on Monday: 24-year-old Ya-Haddy Sisi Saye (also known as Khadija Saye), 65-year-old Anthony Disson, 39-year-old Abufars Ibrahim, and 52-year-old Khadija Khalloufi.
Mr Cundy said the death toll may still change, but not as significantly as in recent days.
Authorities may never be able to identify some of the victims, he said.
Every council and housing association has been ordered to make an urgent lists of buildings that have type of aluminium cladding suspected of speeding up the Grenfell Tower fire in which at least 79 people, including whole families, died.
Panorama reports that ministers were warned on various occasions that fire regulations were not keeping people safe and people living in towers were "at risk".
London Mayor Sadiq Khan said Sunday after attending a church service several blocks from the tower that the fatal blaze was entirely preventable.
Numerous families that were affected lost more than one relative, said Mr Cundy, adding that his "heart went out to them".
Le Corrigé écrit et vidéo du Bac L — Bac de Littérature
Le Monde Campus accompagne les candidats au bac 2017 (bac S, bac ES, bac L et bac STMG), jusqu'aux résultats, le 5 juillet. Même si quelques-uns auraient préféré composer sur l'autre œuvre au programme, les Faux-Monnayeurs d'André Gide.
Mr Cundy's announcement coincided with the police releasing images showing the charred wreckage inside the tower, which show flats reduced to ash and rubble.
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 Islamist extremists in London and Manchester since March.
He said that "it's hard to describe the devastation the fire has caused".
"I would like to reassure everybody that we will be looking at all criminal offences that might have been committed by any individual or any organisation", said Cdr Cundy.
Some 250 police officers are investigating the blaze and a major refurbishment of the tower which was completed previous year.
"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".
"In what I think would of been less than a minute these are all the things I had going through my head".
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