The death toll from the London tower block fire has risen to 17 and the figure is expected to rise further, police said on Thursday.
The fire, believed to have been caused by a faulty fridge on the 3rd or 4th floor of the 24-storey block in the North Kensington district in the early hours, engulfed nearly the entire building in just half an hour, eyewitnesses said.
Search dogs will also be used to help locate the missing in the wreckage.
Cotton had earlier told Sky News it would take weeks to clear the building, and that "tragically now we are not expecting to find anyone else alive". Ministers had been warned several times in the past few years about the panels, which contain a flammable plastic core and have been linked to fires in France and the US.
Meanwhile, 44 households were given emergency accommodation after the blaze. Even though the building was alight from top to bottom and they were in fear of their own lives, they were in and out of that building, committing time after time to rescuing those people that we knew were in there.
It is not yet known what scope the inquiry will be, but Mrs May said it will be in addition to the immediate fire report and any potential police investigation.
Many residents were sleeping as the fire spread, the BBC reported.
Fire Commissioner Dany Cotton said authorities genuinely don't know how many people died and that firefighters have been traumatized by the inability to save more people.
The 8.7 million pounds (9.9 million euro, $11 million) refurbishment also included new windows and heating systems.
Outside the cordons, impromptu tributes appeared with photos of missing people, messages of condolences, flowers and candles.
Kensington and Chelsea Council admitted it had received complaints over the works, after a residents' action group said its warnings about safety had fallen on "deaf ears". Some residents said no alarm had sounded.
"A lot of my firefighters yesterday experienced things they will never have seen before and I've spoken to some people who were truly distressed".