Prime Minister Theresa May has ordered a full public inquiry into the fire that engulfed a west London block of flats, killing at least 17 people.
That figure is expected to rise, as fire chiefs do not expect to find any more survivors in the burnt-out Grenfell Tower, in north Kensington.
People have been desperately seeking news of missing family and friends.
The PM said people "deserve answers" as to why the fire spread so rapidly and that the inquiry "will give them".
Mrs May, who made a brief, private visit to the scene earlier, said: "[The emergency services] told me that the way this fire had spread and took hold of the building was rapid, it was ferocious, it was unexpected.
"So it is right that, in addition to the immediate fire report that will be produced and any potential police investigation, that we do have a full public inquiry to get to the bottom of this."
Labour leader Jeremy Corbyn, also visited the site, telling community leaders "the truth has to come out".
The BBC's assistant political editor Norman Smith said if the inquiry followed the course of previous inquiries, it "may well be headed by a judge".
"It will almost certainly hold its evidence sessions in public and those who will give evidence will include the local council, the builders, the contractors but yes too, I suspect the tenants and the relatives of some of the victims," he added.
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More than 30 people remain in hospital - 17 of whom are in a critical condition.
The Queen earlier said her "thoughts and prayers" are with families
Firefighters were called to the 24-storey residential tower in the early hours of Wednesday, at a time when hundreds of people were inside, most of them sleeping.
Many were woken by neighbours, or shouts from below, and fled the building.
Fire crews rescued 65 adults and children, but some stayed in their homes, trapped by smoke and flames.
At the scene
By Lucy Manning, special correspondent, BBC News
For the families of the missing, grief is mixing with anger.
They are angry at the lack of information about their relatives. Many just don't know if they are alive, dead or injured.
I spoke to one man: His cousin, her husband and their baby are missing.
He is pleading for the police, the hospitals, the authorities to give him information about those who are injured or who might have died.
It's a complaint I've heard from families after terror attacks: that the system doesn't seem to help the families. That the wait is too long and agonising.
His relatives had to trawl round hospitals and, thanks to a nurse, found two missing children but they haven't found the rest of the family.
Although it's hard for the authorities to deal with these incidents his message to the police, hospitals, officials and politicians is "please please help us."
On Thursday morning, London Fire Commissioner Dany Cotton said her crews had identified a "number" of those killed, "but we know there will be more".
Asked how many were still missing, Met Police Commander Stuart Cundy said it would be "wrong and incredibly distressing" to give a number.
"I know one person was reported 46 times to the casualty bureau," he said.
A brief search of all floors in the tower had been carried out, but the severity of the fire and amount of debris meant a thorough search would be "difficult and painstaking", Commander Cotton said.
Sniffer dogs will now be sent in to search for evidence and identification of people still inside, she said.
Temporary structures will be built inside the block in order to shore it up before more thorough work can begin.
The cause of the fire, which took more than 24 hours to bring under control, remains unknown.
Throughout the morning, only wisps of smoke were seen coming from the charred building, but flames were later seen flaring up again on a lower floor.
London-born Adele and her husband visited the scene on Wednesday evening, and the singer was seen comforting people.
Singer Rita Ora pitched in by helping to sort donations outside the tower.
Photographs and messages in English and Arabic have been left for loved ones on a wall of condolence near the tower block.
Alongside them are words of anger and calls for justice, with people saying their safety concerns were not listened to.
The local authority - Kensington and Chelsea council - said 44 households had been placed in emergency accommodation so far.
Throughout Wednesday night, people donated food, clothes and blankets for those left without homes.
By early morning some volunteers said they had been overwhelmed with donations and were turning people and vans away.
The government has said checks were now planned on tower blocks that have gone through a similar upgrade.
Construction firm Rydon, which carried out the refurbishment, initially said in a statement that the work met "all fire regulations" - the wording was omitted in a later statement.
Fire risk assessment in tower blocks was "less rigorous" since responsibility for it shifted from the fire brigade to the owner, Sian Berry, housing committee chairwoman of the London Assembly, said.
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