The Queen and Prince William visited a relief centre for Grenfell Tower fire victims, while the missing could number as many as 76, the BBC understands.
Their visit to the Westway Sports Centre comes after police say some of those killed may never be identified.
Police have confirmed that at least 30 people have died as a result of the blaze at the west London flats.
Metropolitan Police Commander Stuart Cundy said that of those who were killed, one died in hospital.
He also said there was nothing to suggest that the fire was started deliberately, and that everyone in hospital has now been identified.
The fire broke out shortly before 01:00 BST on Wednesday.
The Queen and Duke of Cambridge met volunteers, residents and community representatives.
The Queen paid tribute on Thursday to the “bravery” of firefighters and the “incredible generosity” of volunteers now offering support.
Emergency services are spending a third day searching for bodies in the burnt-out Grenfell Tower in North Kensington.
Fire chiefs say they do not expect to find more survivors. Police have launched a criminal investigation into the fire and PM Theresa May has ordered a public inquiry.
The prime minister – who faced criticism for not meeting survivors of the tragedy on a visit to the scene on Thursday – said the victims “deserve answers”.
Mrs May visited those injured in the fire on Friday morning, and will chair a cross-Whitehall meeting later on how the authorities can help the community recover.
Housing minister Alok Sharma said the government was working with the local authority to ensure that “every single family will be rehoused in the local area”.
But a statement from Kensington and Chelsea Council said, while they were trying to rehouse people in the borough, it is “possible the council will have to explore housing options that may become available in other parts of the capital.”
Six victims of the blaze have been provisionally identified.
However, Commander Cundy has said earlier there was “a risk that sadly we may not be able to identify everybody”.
When previously asked about the number of dead, he said he hoped the death toll would not reach “triple figures”.
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.”
The leader of Kensington and Chelsea Council – the authority that owns the tower block – told BBC Two’s Newsnight it would not use the type of cladding fitted to Grenfell Tower on other buildings in the borough.
The cladding – installed on the tower in a recent renovation – has come under scrutiny, with experts saying a more fire resistant type could have been used.
Cllr Nicholas Paget-Brown also said there had not been a “collective view” among residents in favour of installing sprinklers during the renovations.
Meanwhile, Conservative MP Chris Philp said the public inquiry should produce interim findings to ensure swift action can be taken if residents in other tower blocks are at risk.
On Thursday, the first victim of the fire was named as Syrian refugee Mohammed Alhajali, 23.
The Syria Solidarity Campaign said Mr Alhajali, a civil engineering student, had been in a flat on the 14th floor when the fire broke out, and had spent two hours on the phone to a friend in Syria.
He had been trying to get through to his family while he was waiting to be rescued.
His older brother, Omar, told the BBC he had lost Mohammed on the way out of the building.
At the scene
By Peter Hunt, BBC royal correspondent
This is the British monarchy, in action, showing it has learnt from its mistakes of the past.
Mistakes that have included the significant time that elapsed before the Queen visited the site of the Aberfan disaster in the 1960s and the “Show us you care” newspaper headlines that were printed 20 years ago, in the days following the death of Diana, Princess of Wales.
As Theresa May is learning to her cost, it is a tragedy with a growing political dimension. There is a howl of pain and anger being directed at an establishment which has the royals at its heart.
There’s the talk of the divide between rich and poor. The Queen’s grandson is a millionaire prince living in a palace in the same borough as Grenfell Tower.
In coming to the site, the Queen was acting as “head of the nation” – a focal point at a moment of considerable pain. She was also providing her prime minister with a masterclass in how to respond on such occasions.
Stories of how people managed to escape have also emerged.
Christos Fairbairn, 41, a resident who lived on the 15th floor, described how he collapsed while fleeing the building, only to be rescued by a firefighter.
Meanwhile, it has emerged that Elpidio Bonifacio, a partially blind man in his 70s, was rescued from his 11th-floor flat after having been seen at the window waving a jumper.
His son Gordon, 41, said on Facebook that his father was now in intensive care.
A political row also erupted, after the prime minister made a private visit to the scene, where she spoke to London Fire Commissioner Dany Cotton and members of the emergency services.
However, unlike Labour leader Jeremy Corbyn and London Mayor Sadiq Khan, Mrs May was not thought to have spoken to families and residents.
Downing Street said the purpose of her visit was to get a briefing from emergency services and to ensure that they had the resources they needed.
She later announced a public inquiry, but former cabinet minister Michael Portillo said the prime minister “didn’t use her humanity”.
Mr Khan has written an open letter to the prime minister, saying the community was “understandably distraught, frustrated and increasingly angry”.
He called on Mrs May to set out how she plans to help the community “as a matter of urgency”.
Posts on social media suggest residents are planning to march from Grenfell Tower to Kensington and Chelsea town hall on Friday afternoon.
Rydon, the company that carried out the £8.6m refurbishment of Grenfell Tower, said it welcomed Mrs May’s announcement of the public inquiry.
It said its refurbishment “met all required building regulations as well as fire regulation and health and safety standards”.
Kensington and Chelsea Tenant Management Organisation, which manages the tower for the council, has offered its “sincere and heartfelt condolences” to those affected and said it was working to help the residents of the tower block.
All schools in Kensington and Chelsea have reopened, but two are now operating in other schools.
Kensington Aldridge Academy is running at Burlington Danes in nearby White City.
St Francis Assisi, a primary school also situated inside the cordon at the Lancaster West estate, is operating within Sion Manning School nearby.
On Friday, officials said 24 people remained in hospital – 12 of whom were in a critical condition.
An emergency number – 0800 0961 233 – has been set up for anyone concerned about friends or family.