Cundy said the "complex" and "exhaustive" inquiry will focus on a range of issues including how the building was constructed, a recent refurbishment of it, how it is managed and maintained and fire safety measures.
Commander Stuart Cundy said that number "may increase".
"The residents of Grenfell Tower, families who have lost loved ones, and the emergency services who have been working so hard to help them have been through some of the most harrowing and traumatic experiences imaginable", Theresa May said.
While he refused to speculate on the inquiry's outcome, Cundy said, "I would like to reassure everybody that we will be looking at all criminal offenses that may have been committed by any individual or organization".
The new exterior cladding used in a renovation on London's Grenfell Tower may have been banned under United Kingdom building regulations, two British ministers said Sunday as police continued their criminal investigation into the inferno that killed at least 58 people.
"But, frankly, the support on the ground for families who needed help or basic information in the initial hours after this appalling disaster was not good enough", she said.
By the blackened Grenfell Tower, firefighters took off their helmets and stood still to observe the minute's silence, some with their arms around each other's shoulders.
Experts say the cladding and the insulation it contained seems to have spread the flames quickly along the exterior of the building, overwhelming safety devices like fire doors.
"My understanding is the cladding in question, this flammable cladding which is banned in Europe and the USA, is also banned here", Hammond told the BBC earlier. Metropolitan Police Stuard Cundy said: "Sadly, our work will be ongoing for many, many weeks".
"The bad reality is, as I've said before, is that due to the intensity of the fire and the devastation within Grenfell Tower that we may not be able to identify everybody that died", he said.
A short walk away, however, are apartments and houses that cost millions of pounds and are home to a wealthy elite that residents of the Grenfell Tower had seen as a world apart.
The Metropolitan Police has released footage showing the "indescribable" damage caused by the fire.