Rescuers do not expect to find anyone else alive in the west London block of flats which was engulfed by a massive fire, the fire service says.
London Fire Commissioner Dany Cotton said there were still “unknown numbers” of people in the smouldering ruins of Grenfell Tower, in north Kensington.
People have been desperately seeking news of missing family and friends, after 12 people were confirmed dead.
Police have warned the number of deaths is expected to rise.
PM Theresa May has promised a full investigation, as questions were being asked about the speed at which the fire spread.
Thirty-four people remain in hospital – 18 of whom are in a critical condition.
Firefighters were called to the 24-storey residential tower at 00:54 BST on Wednesday, at a time when hundreds of people were thought to have been 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.
The cause of the fire remains unknown.
Dozens of people left homeless by the fire spent the night in makeshift rescue centres, as well-wishers signed a wall of condolence near the site.
Photographs have been left alongside messages for loved ones.
The local authority – Kensington and Chelsea council – said 44 households had been placed in emergency accommodation so far.
Through the night, people have been donating food, clothes and blankets for those left without homes.
Bhupinder Singh, one volunteer handling donations, said: “It is times like this that the best of our community comes out. This is where you find out how good it is to live in England and how good it is to be a Londoner.”
Questions have been raised about why the fire appeared to spread so quickly and engulf the entire building.
BBC Newsnight’s Chris Cook says the type of cladding on the outside of Grenfell Tower, installed in 2015 during a refurbishment, had a polyethylene – or plastic – core, instead of a more fireproof alternative with a mineral core.
Similar cladding was used in high-rise buildings hit by fires in France, the UAE and Australia, he said.
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.
Concerns have also been raised about fire alarms not going off and the lack of sprinklers.
It is still possible to build tall buildings without sprinklers, said Russ Timpson of the Tall Buildings Fire Safety Network, but he expected regulations might change soon.
Overseas colleagues are “staggered” when they hear tall buildings are built in the UK with a single staircase, he added.
Meanwhile appeals are being made on social media for news of friends and family who are still unaccounted for.
Among them is 12-year-old Jessica Urbano Ramirez, 66-year-old retired lorry driver Tony Disson and security guard Mo Tuccu, who was visiting friends in the tower to break the Ramadan fast.
An emergency number – 0800 0961 233 – has been set up for anyone concerned about friends or family.
Stories are continuing to emerge from those who defied official advice to stay put, and ran with their families down dark, smoke-filled corridors to get out of the building.
Michael Paramasivan, who lives on the seventh floor with his girlfriend and young daughter, said: “If we had stayed in that flat, we would’ve perished.”
Others were concerned that the smoke alarms did not go off.
Zoe, from the fourth floor, said: “The way the fire spread so quickly from the fourth floor, all the way up to the 23rd floor was scary.”
People in the street below described watching as a baby was thrown from a window, people jumped and climbed down the side of the burning tower using ropes made from bed sheets.
Jody Martin said: “I watched one person falling out, I watched another woman holding her baby out the window… hearing screams.
“I was yelling at everyone to get down and they were saying ‘We can’t leave our apartments, the smoke is too bad on the corridors’.”
The prime minister has promised a “proper investigation” into the fire.
But Labour politicians are calling for answers from the government. Labour leader Jeremy Corbyn said: “We need to know what reports were available, what information was given and what actions were taken.”
A review of building regulations covering fire safety was promised by Prime Minister Theresa May’s chief of staff, Gavin Barwell, last year, when he was a government minister, but has not been published.
Responding to earlier reports, the Department for Communities and Local Government said it was “simply not true” that a report has been “sat on”.
Following the Lakanal House fire in south London in 2009, in which six people died, the coroner recommended the guidance relating to fire safety within the Building Regulations was simplified.
The government said this work was “ongoing”.
The government also wrote to councils encouraging them to consider retro-fitting sprinklers, as recommended by the coroner, a statement said.
Southwark Council was fined £270,000 for breaching fire safety regulations after the Lakanal House blaze.