Dozens of people have been reported missing since last Wednesday's early-morning blaze that struck while many who live in the building's 120 apartments were asleep. Experts believe the new paneling, which contained insulation, helped spread the flames quickly up the outside of the public housing tower.
Mr Cundy said the death toll - which increased from 58 - could still change as investigations continue, but not as significantly as it has previously. "So that 58 would include that 30", the spokesman said Saturday.
Officials are using dental records, fingerprints, DNA samples, tattoos and scars to try and positively identify victims.
"It is really important that we are clear about the scale of the challenge facing us as our teams search Grenfell Tower to recover those people still inside and return them to their loved ones". We know that there are still bodies of those who died inside the building and we want to return those people to their families as soon as we possibly can.
On Monday, police confirmed 79 people are either dead or missing and those who are unaccounted for are presumed to be dead.
Members of London's emergency services observe a minutes' silence in memory of the victims of the June 14 fire at the Grenfell Tower block, pictured on the horizon, in Kensington, west London, on June 19, 2017.
But now, The Independent has confirmed that the family have not suffered from any casualties, one the daughters confirmed on Facebook that they were not injured but have lost everything. Composing himself, he said "It's fair to say it is incredibly emotional working in there".
The Metropolitan Police has launched "wide ranging" investigation, looking at the construction of the building, the recent refurbishment, how it was managed and maintained, and fire safety measures.
The government has promised a full public inquiry, but that has done little to a sense of frustration at the lack of information about how the fire moved so quickly to engulf the building.
Labour Party lawmaker David Lammy demanded that the government and police immediately seize all documents relating to Grenfell's renovation to prevent the destruction of evidence that could show criminal wrongdoing.
The fire has prompted warnings about fire safety risks in many other council tower blocks built in the same era.
An additonal 70 people are reportedly missing.
He said five of the dead had been formally identified, and it would be a slow and painstaking task to identify the others because of the intensity of the fire.
More than 200 firefighters and 40 fire trucks were involved in operations to douse the blaze, which last for several hours.