LONDON — The number of people who died in London’s Grenfell Tower fire may be slightly lower than the 80 previously estimated, police said Tuesday, also announcing that individuals may face manslaughter charges over the blaze.

Metropolitan Police Commander Stuart Cundy said the final figure might “come down a little,” but will not be known until police have completed a painstaking search of the charred building. He said that so far 60 victims of the June 14 blaze have been formally identified.

Police also said for the first time Tuesday that they will consider manslaughter charges against individuals over the fire. The force has previously said it has “reasonable grounds” to suspect local authorities may have committed corporate manslaughter.

Detectives are also investigating eight cases of fraud involving people who claimed to have relatives or property in the building, and four possible cases of theft from apartments after the fire.

Updating reporters on the investigation, Detective Chief Inspector Matt Bonner said the investigation would deal with “whatever offenses come to light.”

“The kind of stuff I would envisage we may come across would involve offenses perhaps of fraud, misconduct offenses, health and safety breaches, breaches of fire safety regulations, and of course offenses of manslaughter, whether that be on a corporate or an individual level,” he said.

The blaze began in a refrigerator in an apartment at Grenfell Tower before racing through the 24-story building. A public inquiry — separate from the police investigation — has begun to find out how a small fire was able to spread so quickly, becoming Britain’s deadliest blaze in decades.

Many residents accuse officials in Kensington and Chelsea, one of London’s richest boroughs, of ignoring their safety concerns because the public-housing block was home to a largely immigrant and working-class population.

One focus of investigation is the role of combustible aluminum cladding installed during a refurbishment to the 1970s tower block. Emergency safety checks have uncovered scores of other buildings across Britain with similar cladding.