"We are looking at every criminal offence from manslaughter onwards," Fiona McCormack from London's Metropolitan Police said at a briefing on the June 14 blaze in west London, which left 79 people presumed dead.
Referring to the tiles and insulation on the outside of the building, which have been widely blamed for the rapid spread of the flames, she said: "All I can say at the moment is they don't pass any safety tests."
The cladding was installed on the 24 storey council owned Grenfell Tower, which was built in 1974, as part of a refurbishment completed last year.
It has prompted a wider review of social housing which has identified at least 600 towers in England with similar cladding.
McCormack said police had also established that the fire started with a faulty fridge, a Hotpoint FF175BP model.
She said the model had not been subject to any product recall.
McCormack said police were investigating companies involved in the building and refurbishment of the tower, and possible 'health and safety and fire safety offences'.
She said all 'complete bodies' had been removed and there was 'a terrible reality that we may not find or identify everyone who died due to the intense heat'.
The officer also repeated calls for any members of the public with information about people who may have been in the tower at the time of the blaze to come forward.
Police fear the toll may be higher because some residents may have been living in the tower illegally.
"Our forensic search may not be complete until the end of the year," she added.
Prime Minister Theresa May stressed on Thursday that all Grenfell victims, regardless of their immigration status, would be able to access whatever help they need.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)