The images of Syrian refugee Mohammed Al Hajali, who was the first victim named, were some of the many painful photographs that have been released in the days since the fire.
"There is considerable damage within Grenfell Tower", he said.
"And our priority is to bring out those who are still in there".
The 91-year-old monarch said that Britain remains "resolute in the face of adversity" after the horrendous fire and recent extremist attacks in London and Manchester.
Fifty-eight people who were in Grenfell Tower are still missing and are presumed to be dead, London police announced Saturday, raising the death toll in the horrific inferno that turned the public housing block into a charred hulk.
"I believe there are 79 people that are either dead, or missing, and sadly I have to presume are dead", Metropolitan Police Commander Stuart Cundy told reporters.
Each family will be offered support from their own named mental health practitioner, in addition to police family liaison officers. Counselors are already working with 52 families.
Some of the anger stems from reports that Grenfell Tower had no central sprinkler system and was built with flammable materials that residents told the government needed to be fixed.
"That number 58 may change". I really hope it won't, but it may increase.
She added: "I have ordered that more staff be deployed across the area, wearing high visibility clothing, so they can easily be found, dispense advice and ensure the right support is provided". "It might be that some of those are safe and well but for whatever reason have not reached (out) to let us know".
"We have colleagues in there as we speak, searching for and recovering those that have died".
"It may take longer than that. But we need to make sure that that actually happens", she added. Events in London remind us once again that we must be unstinting in our pursuit of the best possible building control laws to avoid tragedy in the future.
"When the truth comes out about this tragedy, we may find that there is blood on the hands of a number of organizations", Lammy said.
"The investigation will be exhaustive".
"The prime minister is very aware that people want answers promptly and we want to get this going promptly, so that's our intention", the spokeswoman said.
"If there are any safety issues that we, and other experts we will be using, identify, we will share that immediately".
The search of the 24-floor building had been paused on Friday due to safety concerns, but has now resumed, Cundy said.