Hands cautioned Sunday that investigators still don't know exactly what cladding was used when the building renovation was completed a year ago.
"There are 58 people who we have been told were in Grenfell Tower on the night that are missing and therefore, sadly, I have to assume that they are dead".
Metropolitan Police Commander Stuart Cundy warned that the death toll could rise further as he formally identified a first victim as 23-year-old Mohammad Alhajali.
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".
"Grenfell is where they shove all the people who don't have any choice", said a resident as he watched his home burn.
He says it may be necessary for numerous outmoded tower blocks built in the 1970s to be demolished because of safety concerns.
"Whilst our teams have been from the bottom to the top of the tower, we must now carry out a full forensic and systematic search". He says "my heart goes out to those affected".
Mrs May later said that all survivors would be rehoused within three weeks as close as possible to the tower. A new sign was put up, removing that detail.
The official death toll from the blaze now sits at 30, up from 17 overnight, as firefighters continue the extremely hard process of recovering bodies from within the tower.
His call was echoed by London Mayor Sadiq Khan who wrote an open letter to Theresa May demanding that she confirm "as a matter of urgency" that everyone from Grenfell Tower and other evacuated properties "will be rehoused locally immediately".
The fire occurred early Wednesday morning, quickly spreading through the 20 storey block. Police have established a security cordon around the building to protect public safety and allow searchers easy access to the wrecked building.
Theresa May is "distraught" by the Grenfell Tower block fire, her most senior minister has said ahead of a meeting with survivors of the disaster at Downing Street.
"Everyone affected by this tragedy needs reassurance that the Government is there for them at this bad time - and that is what I am determined to provide". We are not stupid we are aware people are dead. She also chaired the government's Civil Contingencies Committee, which deals with major crises such as terrorism or natural disasters, in Whitehall.
One demonstrator held a placard, which said simply: "I'm livid".
The tragedy destroyed much of the west London apartment block on June 14 and claimed the lives of at least 58 people.
Dozens are still missing.
She said earlier that the national mood is somber but that Britain is resolute in the face of adversity.
The queen's official birthday is marked in June when the weather is often nicer than in April, the actual month of her birth.
At least 30 people have died in Wednesday's fire and dozens are missing.
Some 19 people remain in four London hospitals, 10 of who are in critical conditions.
Meanwhile, fury has grown in the local community at what people say is a slow response from authorities and a failure to inform families and friends about the fate of loved ones.
The tragedy has provoked a huge response from nearby communities. More than 3 million pounds ($3.8 million) have been raised for the victims.
Public anger was mounting as residents and neighbors demanded answers for how the blaze spread so quickly amid reports that contractors installed a cheaper, less flame-resistant type of exterior paneling in a renovation of Grenfell Tower that ended in May 2016.
The identification of the victims is proving very hard - which experts attribute to the extreme heat of the fire.
Ms May has announced a public inquiry into the fire which would be fast-tracked. It followed a separate, smaller protest at Kensington Town Hall, where residents tried to air their grievances to councillors.