Cundy said a criminal investigation began the day of the fire and will look at a "wide range" of issues, including the renovation project, the public housing block's management and maintenance, and fire-safety measures.
"Whilst I've said I think there may be changes, I don't think those changes will be as significant as the changes we've seen over the last few days", he said.
He said police will release images and video from inside the tower tomorrow, pending the approval of Grenfell families.
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'Equally, there may be people who thankfully may have managed to escape the fire and for whatever reason have not let their family or friends or police know, ' he said.
Mr Cundy said: "The investigation will be exhaustive".
Fire had ripped through the 24-storey residential block in north Kensington in the early hours of June 13, trapping hundreds of people inside.
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"Sadly at this time there are 58 people who we were told were in Grenfell Tower on the night, who were missing, who I have to assume are dead".
British outlets said May struggled to offer support or leadership in the wake of the blaze, accusing her of lacking emotional intelligence and calling her "Maybot". The paneling has been blamed for quickly spreading the flames. "We will go where the evidence may take us".
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.
"We have rigorously tested the cladding that has gone onto our buildings to an extent that it fits and meets all fire safety regulations", he said.
He said: "We must also prepare people for the awful reality that some people may not be identified due to the intensity of the fire". She also said she will receive daily reports from the stricken neighborhood.
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The Metropolitan Police has released footage showing the "indescribable" damage caused by the fire.