Fire Commissioner Dany Cotton warned it would be a "very slow and painstaking" process to reach all of those caught in Wednesday's inferno.
"The building itself, the core of it is structurally sound at the moment, so the firefighters have been going in", she said.
As anger grew over the failures over fire safety, Tottenham Labour MP David Lammy said "arrests" should be made over what he branded "corporate manslaughter".
On Thursday, she met with emergency services at the wreckage of the west London tower, ahead of a visit by opposition leader Jeremy Corbyn.
But it was another politician who led the calls for those responsible for the upkeep of the building to face criminal action.
Survivors told how they fought through black smoke to escape via the central stairwell, which was "littered" with bodies.
More than 30 people are still being treated in hospital, with 17 described as being in a critical condition.
"Every single person living in a high rise building will be frightened, will be traumatised, and will be very, very anxious".
Construction for the building was completed in 1974 and it underwent a renovation that was completed in May 2016.
One focus of the investigation is expected to be the building's rain-screen cladding that was installed for better insulation during the almost 10-million-pound refurbishment work carried out on the building previous year.
Tensions are rising as a group of agitators gather near the burned remains of the 24-storey Grenfell Tower.
"It is a truly terrifying thought but the Grenfell Action Group firmly believe that only a catastrophic event will expose the ineptitude and incompetence of our landlord", the Grenfell Action Group wrote.
Authorities may need to ban the cladding used on the outside of Grenfell Tower, experts have said. The statement did not address the residents' allegations.
Many questions are still unanswered, chief among them, how the fire spread so quickly.
"The size of this building, it could weeks".
"London's fire commissioner says it would be a miracle if anyone is still alive inside", Larry Miller reports for NPR from London.
The cladding - metal panels that were stuck on the outside of the building to help insulate and spruce up the building - has been blamed for the shockingly rapid spread of the fire up and across the building.
It said that developers needed to work harder to ensure that cladding is non-combustible and didn't pose too much of a risk to people living inside. While other materials can buckle in high temperatures, concrete structures can help to prevent building collapse in case of fire, as well as making it safer to use helicopters - which can dump up to 9842 litres of water at a time - to extinguish a blaze. "They woke up and were still trapped in that building and no-one could get out", he said.
Volunteers and charities helped feed and shelter people who could not return to their homes overnight.
The local council has been inundated with so many donations of food and supplies that by Thursday morning it had run out of space, and said no more could be accepted.
But others defended her, including @nichoals_zara, who tweeted: "The fact Adele went to Grenfell Tower to try & help & didn't make any fuss or court any publicity around it shows how down to earth she is". She could also be seen loading bottles of water and food into vans.