Fire had ripped through the 24-storey residential block in north Kensington in the early hours of June 13, trapping hundreds of people inside. Police had earlier put the toll from Wednesday's inferno at 58 presumed dead.
Aluminum cladding with insulation sandwiched between two panels has been blamed for helping to spread flames in major fires in many parts of the world, including blazes in the Middle East, Europe, Asia and the United States.
One of them, Chancellor Phillip Hammond, a senior member of May's cabinet, told the BBC that investigators were looking at several possibilities.
The fire has also been transformed into a symbol of class inequality - the Grenfell Tower's charred remains stand high above one of the British capital's wealthiest neighborhoods.
"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 Sunday. Hands cautioned that officials don't yet have exact details about the renovation that ended just a year ago.
A day after the deadly incident, Housing Minister Alok Sharma told MPs the government "will guarantee that every single family from Grenfell Tower will be re-housed in the local area".
Flowers and missing people posters are taped to the gates of the church, which has been used as a relief centre in the wake of the blaze, while bags of donations including nappies and clothes are piled outside the door.More news: Theresa May condemns 'sickening' terror attack on Muslims
More news: Karen Handel Falsely Suggests Jon Ossoff 'Has $30 Million Behind Him'
More news: The intensifying strangeness of US-North Korea relations
Residents who survived said they warned the building's manager about fire hazards for years but were ignored, Vigliotti reported.
David Lammy said Sunday he is anxious that documents will be quietly deleted and disposed of as police begin a search for evidence.
"The response of the emergency services, NHS and the community has been heroic", she said in a statement.
Rydon, the company that carried out the recent refurbishment, said the "project met all required building regulations". He says trust in the authorities is "falling through the floor".
He said: "We investigate criminal matters".
Residents want answers on why the fire spread so quickly, trapping numerous estimated 600 residents.
"Our focus has been on those that we know were in Grenfell Tower".
He said the situation has become an emergency and that "all assets" should be brought to the table. "However, there may be other people who were in there on the night that others were not aware were there", he said. At least 58 people are believed to have died in the blaze.
"But being with colleagues from the London fire brigade when I was in there, colleagues from the London ambulance service and other police officers, I think it's fair to say it is incredibly emotional working in there".