Theresa May has ordered more boots on the ground at the Grenfell Tower fire site after labelling the support given to families in the aftermath of the deadly blaze "not good enough".
Police said at least 58 people died, or are missing, presumed dead, after fire ravaged the 24-storey tower block in the early hours of Wednesday.
Commander Stuart Cundy of the Metropolitan Police warned that the death toll could rise further as he formally identified the first victim as 23-year-old Syrian refugee Mohammad Alhajali.
At 58 casualties, it would make the Grenfell Tower blaze the deadliest in the capital since the Second World War.
The Prime Minister, who "welled up" after hearing harrowing accounts from people caught up in the deadly fire, said there had been "huge frustrations" on the ground as people struggled to find information.
More than 250 firefighters tackled the blaze in north Kensington as London Fire Commissioner Dany Cotton said the scene looked like a "disaster movie".
Speaking to the Observer, she said crews did not follow normal practice, adding: "Had we just followed standard fire brigade procedures, we would not have been able to commit firefighters in and conduct the rescues we did."
Sixteen bodies have been taken to the mortuary after flames tore through the 1970s tower block - while 14 others have been recovered from the building.
Moving tales from those caught up in the disaster are continuing to emerge, including a five-year-old girl who was swept up by her mother's boyfriend as black smoke filled her seventh floor bedroom.
Thea West, who was rescued by Mickey Paramasivan, told the Sun on Sunday: "Mickey woke me up. He's my hero. He put me under his dressing gown and ran down the stairs.
"There was smoke everywhere and it was too strong. I could not breathe."
Mr Cundy said: "Sadly, at this time there are 58 people who we have been told were in the Grenfell Tower on the night that are missing, and therefore sadly, I have to assume that they are dead."
"That number 58 may change. I really hope it won't, but it may increase.
"My commitment to families is that as soon as we can, we will locate and recover their loved ones.
"The reason we had to pause the search and recovery yesterday was for the safety of our staff.
"We do not want another fatality arising out of this tragedy."
Police have appealed to anyone who may have escaped from the building, but has not yet come forward, to make themselves known.
When asked about the search, Mr Cundy replied that the officers had gone "all the way to the top" of the tower, and explained that the first phase was a visual search.
Mr Cundy said the police investigation into the blaze would look at the building and its refurbishment in 2016 and vowed to prosecute people if there was evidence.
The police are appealing to anyone with pictures or videos of the blaze to hand them in, as they may help establish not only where and how the fire started, but also how it spread.
Victims met the Prime Minister at Number 10 on Saturday evening and man representing the group said they had spoken about their "demands and what we expect".
Mrs May said she had fixed a deadline of three weeks for everybody affected to be rehoused locally.
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."
Family liaison officers are working with 52 families, and as soon as victims are identified, their loved ones will be told.
Mr Cundy said: "I absolutely understand the frustration of why figures haven't been released earlier. The reason for that - at one point, in terms of our casualty bureau, there were 400 people who were reported missing from Grenfell Tower.
"Grenfell Tower itself is 120 flats. We have worked tirelessly over the last four days to truly understand those that we know were there on the night."
Anger flared in the Kensington community over the weekend - with many protests taking place across the capital - as some accused the authorities of withholding information and responding inadequately.
Mr Cundy said: "The investigation will be exhaustive. My intention is that it will help provide answers.
"If, as we investigate, we identify issues that are a risk to public safety, we will not be waiting until the end of the investigation before we provide that information to the appropriate authorities.
"If there are any safety issues that we and experts that we will be using identify, we will share that immediately."
Eve Allison, a Conservative who sits on Kensington and Chelsea Borough Council, said it would have been "ideal" if refurbishments to Grenfell Tower had looked at both the outside and the inside of the building.
She told BBC Breakfast: "The mood is sombre and the community continue to do what we can. The danger is when hope starts to fade, and from hope then what you'll find is despair.
"It is on our watch, it's our responsibility, we do have a duty of care to all our residents and whatever findings and failings come out, they have to come out soon because all the community, the victims, the families, people need answers.
"All too often we're a little bit too concerned with how the immediate streetscape looks, how a building fits into other buildings, does it detract from the immediate streetscape.
"I was not involved with the actual planning of the recent refurbishment... from what I'm hearing, it would have been ideal if part of the refurbishment package had looked at actually trying to gentrify inside, not just outside."
NHS England said 18 patients remained in hospital after the fire including nine who are in critical care.
The hospitals providing care include King's College, Chelsea and Westminster, the Royal Free and St Mary's.
Commons leader Andrea Leadsom said Mrs May had decided to send in senior civil servants to deal with the aftermath so "issues can be addressed much more quickly and with greater experience and precision".
Asked if she felt a sense of shame over the disaster, she told BBC One's Sunday Politics: "Totally, yes, of course, of course.
"We all think what should we have done, could we have done? It's just unbearable. This cannot happen in the 21 century and yet it has."