The Grenfell Tower fire started in a faulty fridge and the cladding and insulation on the block has failed safety tests, police said.
Metropolitan Detective Superintendent Fiona McCormack said the Hotpoint FF175BP model had not been subject to any product recall.
Witnesses at the scene of the 24-storey blaze in north Kensington on June 14 described hearing one resident claiming it was his appliance which was responsible.
The number of people to have died, including those classed as missing presumed dead, remains at 79, she said.
Ms McCormack said the tests carried out as part of the investigation were "small scale", but added: "All I can say at the moment is they (tiles and insulation) don't pass any safety tests.
"What we are being told at the moment by the Building Research Establishment is that the cladding and insulation failed all safety tests."
She added: "Our investigation is to establish how the fire started."
Manslaughter charges are among a string of offences being considered by police as part of the investigation, Ms McCormack said.
Documents and materials had been seized from a "number of organisations", she added.
She said: "We are looking at every criminal offence from manslaughter onwards, we are looking at every health and safety and fire safety offences and we are reviewing every company at the moment involved in the building and refurbishment of Grenfell Tower."
Ms McCormack repeated calls for members of the public with information about people who may have been in the tower at the time of the fire to come forward.
It follows calls, backed by London mayor Sadiq Khan, for an amnesty on people who may have been living in the tower illegally.
Ms McCormack said: "Every complete body has been removed from the building.
"What we are dealing with now, as you can imagine in the intense heat, is a very distressing scene.
"What we haven't got is a picture of how many people might have been in there.
"That's the number in really worried about, that there might have been other innocent people in there."
Describing how the investigation was proceeding, she added: "We have been in Grenfell Tower, from top to bottom, last week.
"Next week we will be installing a lift to the outside of the building to assist. But our forensic search may not be complete until the end of the year."
Repeating concerns from police commander Stuart Cundy about the scale of the task in identifying the victims, Ms McCormack added: "There is a terrible reality that we may not find or identify everyone who died due to the intense heat."