At least 58 people may have died in the massive fire that engulfed a 24-storey residential tower housing over 100 families in west London, Scotland Yard said on Saturday, warning that the casualty figures "may increase".
Metropolitan Police Commander Stuart Cundy said that number "may increase" further and that the "significant" recovery operation is likely to take weeks.
"As soon as we can, we will locate and recover loved ones," he said.
In her traditional birthday message, the 91-year-old monarch made a reference to the "succession of terrible tragedies", a day after she paid a visit to people affected by the massive Grenfell Tower blaze in west London.
She said: "Today is a traditional day of celebration. This year, however, it is very difficult to escape a very sombre national mood.
"Put to the test, the United Kingdom has been resolute in the face of adversity."
She said that during her recent visits to Manchester, the site of the suicide bombing last month which claimed 22 lives, and London - the scene of a terror attack earlier this month and most recently the massive fire - she has been "profoundly struck by the immediate inclination of people throughout the country to offer comfort and support to those in desperate need".
"United in our sadness, we are equally determined, without fear or favour, to support all those rebuilding lives so horribly affected by injury and loss," she said.
Meanwhile, firefighters continue their search at the site of the fire in North Kensington, where a 24-storey residential block was burnt to the core within minutes early on Wednesday.
The blaze tore through all floors of the building and took more than 200 firefighters 24 hours to bring it under control.
Grief has since given way to anger as protests were held in London on Friday by residents demanding more support for those affected by the fire.
Between 50 and 60 people stormed Kensington and Chelsea Town Hall as members of the public demanded the council, which owned the tower blocks, to give reassurances to the victims.
Dozens of demonstrators surged towards the entrance and there were scuffles outside as organisers appealed for calm.
British Prime Minister TheresaMay has faced criticism for not meeting survivors in the immediate aftermath of the major fire, which has rendered hundreds homeless, unlike Labour leader Jeremy Corbyn and London mayor Sadiq Khan who met with the locals on their site visits.
She sought to combat some of the criticism with a meeting with residents, victims, volunteers and community leaders at Downing Street today.
The first secretary of State in her Cabinet, the equivalent of deputy PM, Damien Green came to her defence.
"She has the same degree of sympathy and horror at these events that we all have. We are all desperately sad, we are angry, but of course none of us as angry as those who were directly affected. I absolutely get why they are angry," he said.
Corbyn has written an open letter to the Prime Minister, calling for the public inquiry to ensure "all necessary lessons are learned".
May has committed five million pounds for clothes, food and emergency supplies as part of Grenfell Tower Residents' Discretionary Fund on Friday, which includes the aim to re- house residents within three weeks as close to where they lived before as possible, to pay for temporary housing in the meantime and to provide extra financial assistance.
"The government is making money available, we are ensuring we are going to get to the bottom of what has happened, we will ensure that people are re-housed. We need to make sure that actually happens," she said.
"This was a terrible tragedy that took place. People have lost their lives and others have lost everything. What we are doing is putting in place the support that will help them," she added.
Scotland Yard is leading the criminal investigation into the fire at Grenfell Tower to establish the exact cause of the fire.
The UK government has already announced a full judge-led public inquiry in an attempt to learn lessons from the tragedy and implement any necessary fire measures in other residential towers blocks.