Residents who met the Prime Minister in Downing Street following the Grenfell Tower fire have criticised estate managers of the building as having been "invisible in the aftermath of the tragedy".
Finance minister Philip Hammond said the inquiry would examine whether the regulations banning certain types of cladding were right and whether they were complied with.
The government has said it is carrying out an "urgent inspection" of roughly 2,500 similar tower blocks across the country to assess their safety.
"The bottom line: Sprinklers, fire doors and multiple stairwells work", said Chicago Fire Department Battalion Chief Michael Conroy.
Although police did not speculate on the eventual number of fatalities, local community sources say at least 70 from Grenfell Tower are still missing, including entire families.
It was reported that the material used in the cladding covering Grenfell was Reynobond PE - a cheaper, more flammable version of two available options.
May also said that a public inquiry that is looking into the Grenfell Fire will report directly to her and that she has asked for daily updates from the neighbourhood to be sent to her. British media have reported that contractors installed a cheaper, less flame-resistant type of exterior paneling on the 24-story tower in a renovation that was completed just a year ago. The building was gutted by a fast-moving fire early Wednesday, claiming at least 58 lives.
Meanwhile, Queen Elizabeth II struck a mournful tone in an address to mark her official birthday Saturday, remarking not only on the blaze at the high-rise building but also on the recent terrorist attacks in Manchester and London. But the tower, built in 1974, contained 120 apartments, according to its management company, the Kensington and Chelsea Tenant Management Organization.
London Mayor Sadiq Khan wrote to May on Friday, saying residents felt increasingly enraged and frustrated by the slow response from the authorities.
"People raised these concerns, people were expressing issues regarding the safety and risky living conditions", said Lancaster West Residents Association chairwoman Olesea Matcovschi.
Thirty people have been confirmed dead following the devastating inferno in north Kensington, with a further 28 missing and presumed dead.
He said police would consider criminal prosecutions if there is evidence of wrongdoing and that the police investigation would include scrutiny of the renovation project at the tower, which experts believe may have left the building more vulnerable to a catastrophic blaze.
Many in the United Kingdom are upset with Prime Minister Theresa May for her response - or lack thereof - to the Grenfell Tower fire.
He said they were offering food and other aid and that there was now a single point of contact for help. He says trust in the authorities is "falling through the floor". Hands cautioned that officials dont yet have exact details about the renovation that ended just past year.
Labour Party leader Jeremy Corbyn has called for homes to be " requisitioned if necessary" to house those left homeless by the disaster: "It is hardly acceptable that in London you have luxury buildings and luxury flats kept empty, as land banks for the future, while the homeless and the poor look for somewhere to live".