The type of cladding used on the exterior walls of a London tower block that went up in flames this week was not graded fire-resistant and its use is restricted in the United States, British media reported on Friday.
Instead, she said: "Something awful has happened".
Mr Cundy said the victims included one person who had died in hospital. "There is no timeframe for when the inquest will be, but certainly not in the short term". A public inquiry could take place before the inquests.
Britain's Queen Elizabeth visited residents, volunteers and emergency services at a center helping those affected by London's tower block fire on Friday, with grandson Prince William promising to return to hear residents' concerns.
After her visit, Mrs May said: "Everyone affected by this tragedy needs reassurance that the Government is there for them at this awful time - and that is what I am determined to provide". "They need some answers this summer".
While 30 people have been confirmed dead, there are fears the death toll could hit hundreds. "I do believe the number will increase", police commander Stuart Cundy told reporters in front of the charred Grenfell Tower.
"We need to know what happened", May said in a televised statement.More news: Kabul protest that left several dead enters second day
He added: "We as the police, we investigate criminal offences - I am not sitting here and saying there are criminal offences that have been committed, that's why you do an investigation, to establish it".
Al Manar, a mosque in North Kensington where Grenfell Tower is located, has cancelled i'tikaaf (retreat in a mosque during Ramzan) so that victims can stay there. But, he said, this could take many weeks.
She met injured survivors in hospital yesterday. Twenty-four people are still hospitalized, 12 of whom are in critical condition.
Detectives have asked for early guidance from the special crime division of the Crown Prosecution Service, which is understood to involve any charges that might be considered and the evidence required to bring any prosecutions.
"We are in the richest borough in the United Kingdom and in this very borough we have a building where some of the poorest live and the safety measures are totally inadequate", said Mustafa Al Mansur, one of the organisers of the demonstration. "You get a lot of fragmentation of bodies, charring of bones and sometimes all that's left is ash", said Peter Vanezis, a professor of forensic medical sciences at Queen Mary University in London.
Police were called to the building and formed a barrier to control the situation. "All have a duty of care".
For resident Soran Karimi, 31, who lives in the block opposite, it was nothing short of "murder" and "people should be prosecuted for this". "As soon as we can, we will share that with the families and wider community".