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.
Thirty-four people remain in hospital – 18 of whom are in a critical condition.
The Queen said her “thoughts and prayers” were with families who had lost loved ones and the many still critically ill in hospital.
Prime Minister Theresa May, who is visiting the scene, has promised a full investigation, as questions are asked about the speed at which the fire spread.
Latest updates: Death toll expected to rise
What we know so far
Baby caught after being ‘dropped to safety from tower’
Firefighters were called to the 24-storey residential tower at 00:54 BST on 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.
On Thursday morning, Fire Commissioner Ms Cotton 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”.
The building is to be shored up before more thorough work can begin inside.
The cause of the fire, which took more than 24 hours to be brought under control, remains unknown.
Dozens of people left homeless spent the night in makeshift rescue centres, as well-wishers signed a wall of condolence near the site.
London-born singer Adele and her husband visited the scene on Wednesday evening, and was seen comforting people. Singer Rita Ora also pitched in, helping to sort donations outside the tower.
Photographs and messages in English and Arabic have been left for loved ones.
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.
Through the night, people have been donating food, clothes and blankets for those left without homes. By early morning some volunteers said they were overwhelmed with donations and were turning people and vans away.
One volunteer Bhupinder Singh 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 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.
Roy Wilsher, chair of the National Fire Chiefs Council, said that if the fire spread up the outside of the tower, sprinklers might not have made a difference.
Design and regulations for such tower blocks mean fire should be contained in a single flat, he said. “Clearly something’s gone wrong in this case.”
Meanwhile, appeals are being made on social media for news of friends and family who are still unaccounted for.
Among them are 12-year-old Jessica Urbano Ramirez and 66-year-old grandfather Tony Disson, from the 22nd floor.
Security guard Mo Tuccu, who was visiting friends in the tower to break the Ramadan fast, is also missing.
One family from the 17th floor has five people missing. Husna Begum and four other family members were last heard from two hours after the fire started.
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’.”
- Grenfell Tower, North Kensington
20 residential levels
4 mixed levels of community areas and residential flats
2016 refurbishment completed.
The prime minister has promised a “proper investigation” into the fire, but Labour politicians are calling for answers from the government.
A review of building regulations covering fire safety was promised by Theresa May’s chief of staff, Gavin Barwell, last year, when he was a government minister, but has not been published.
Responding to reports, the Department for Communities and Local Government said it was “simply not true” that a report has been “sat on”.
Cabinet minister David Gauke said: “We are going to need to look very closely at precisely what has happened to see whether there are measures to ensure that nothing like this should happen again.”
Following the 2009 Lakanal House fire in south London, in which six people died, the coroner recommended fire safety guidance in the Building Regulations was simplified.
The government said this work was “ongoing” and it had written to councils encouraging them to consider retro-fitting sprinklers, as recommended by the coroner.
Southwark Council was fined £270,000 for breaching fire safety regulations after the Lakanal House blaze.