Sixteen bodies have been removed from the blackened, 24-story public housing unit, and the first victim was formally identified as Mohammed Alhajali, 23, a Syrian refugee.
The identification of the victims is proving very hard - which experts attribute to the extreme heat of the fire.
British health authorities say they are still treating 19 patients, 10 of whom remain in critical condition after the London high-rise fire.
He also said the last flames had finally been extinguished, two days after the fire broke out early on Wednesday in a working-class enclave of the wealthy Kensington district. And sorrow is quickly turning to anger over whether the building met fire and safety regulations.
May said after the meeting there have been "huge frustrations" in the community as people tried to get information about the fire investigation.
Also on Friday, the Queen and the Duke of Cambridge met volunteers, local residents and community representatives while visiting Westway Sports Centre, near the charred remains of the tower block in north Kensington.More news: Portuguese radio says 25 people killed in forest fires
Facing flak for not meeting with locals sooner, May was set to visit the injured in hospital yesterday, as pressure mounted on her after a failed poll gamble.
Protesters walk down Ladbroke Grove in west London. He said he was "heartbroken by the tragic fire and the appalling loss of life".
The tragedy has provoked a enormous response from nearby communities that have donated food and shelter to the victims. More than 3 million pounds ($3.8 million) have been raised for the victims. Numerous displaced are living in churches and community centers.
People were demanding homes be found urgently for families made homeless by the blaze.
The London Evening Standard reported that hundreds of activists marched to the town hall and gathered outside the building on Friday chanting: "We want justice".
Communities and Local Government Secretary Sajid Javid said inspections of similar buildings had been ordered, with particular attention to the modern cladding used to beautify and add insulation to ageing concrete and steel structures.More news: Pierce backs fearless Latvian to outlast Timea
The use of flammable cladding in tall buildings is banned in some countries, including the U.S. and Germany.
A resident in a nearby building watches smoke rise from a building on fire in London, Wednesday, June 14, 2017.
"The package of support I'm announcing today is to give the victims the immediate support they need to care for themselves and for loved ones", she said, according to the Downing Street statement on Friday.
"We were seeking a change to the building regulations for that very objective".
Mr Green said the probe will look at whether sprinklers should be retrofitted to tower blocks and the Government will "follow the recommendations of the public inquiry". During the video, Rania is seen leading people in the smoke-filled corridor into her apartment for shelter to ensure their safety.More news: Russian Federation inquiry: I'm under investigation
- Defending champion Johnson out of US Open
- Top aides talked Trump out of firing Mueller
- New Analyst Ratings For Big Yellow Group (LON:BYG)
- Champions Trophy final: Players look within before big game
- Kershaw wins, Bellinger hits 2 homers as Dodgers top Indians
- EU says divorce bill, citizens' rights focus of Brexit talks
- Senate approves new Russia sanctions
- Obamas invited to be honorary football coach at University of MI
- Sarfaraz vows to play 'attacking cricket' in clash against India
- London highrise fire: 58 missing, presumed dead, police say