London Police said on Monday that 79 people are presumed to have been killed in the Grenfell Tower fire.
Commander Stuart Cundy said the death toll, which has risen from 58, may still change, but not by as much as it had in recent days.
Photos and videos published by the Metropolitan Police show the gutted wreckage of apartments within the 24-storey tower block after Wednesday's fire.
The deadly blaze in the social housing block has led to growing public anger.
The 1974-built concrete tower had recently been fitted with new exterior insulation cladding, which many locals blame for spreading the inferno so quickly.
Cundy promised an "exhaustive" criminal investigation into the fire that would also look at a major refurbishment of the building completed last year.
"We will go where the evidence may take us," and do everything possible "to ensure that those responsible will be brought to justice," he said.
"If I identify... an issue that is a risk to public safety, we will be sharing that immediately with the relevant authorities," he added.
The government has set up a £5 million emergency fund for the Grenfell Tower residents, allocating a minimum £5,500 to each household with £500 cash payments already being handed out.
