With the death toll rising, families of the victims have railed against officials like May and Mayor Sadiq Khan.
Meanwhile, police and firefighters have now reached the top of the tower in their search. He says "my heart goes out to those affected".
He reiterated there is a police investigation underway and that it will look at how the fire spread.
Jeremy Corbyn has called on his supporters to "occupy" empty buildings to find homes for victims of Grenfell Tower fire. A new sign was put up, removing that detail.
In a television interview, the Prime Minister said the fire was "absolutely horrifying" and had been a "terrifying experience" for those affected.
Major roads near the stricken building were open Saturday.
British Prime Minister Theresa May has sidestepped questions over her response to the disaster, after facing criticism of her reaction to the tragedy. May was criticised for not meeting with the victims and those displaced by the fire, with the offical line from her office claiming it was due to " safety concerns". The reason for that - at one point, in terms of our casualty bureau, there were 400 people who were reported missing from Grenfell Tower.
Activists and local residents held demonstrations at the borough's town hall, London's Oxford Street, the United Kingdom home office, the BBC, and the prime minister's official residence at Number 10 Downing Street to vent their frustrations.
The queen and her husband, Prince Philip, stood silently on the steps of Buckingham Palace before the start of the Trooping the Color ceremony that each year marks the queen's official birthday, which is traditionally celebrated in June when the weather is warm.
"They have been left with nothing - no bank cards, no money, no means of caring for their children or relatives", the prime minister said in a statement Friday.
On Saturday, NHS England said 19 people were being treated in hospital, including 10 in critical care. Grief over a high-rise tower blaze that killed dozens of p.
The tragedy has provoked a big response from nearby communities that have donated food and shelter to the victims.
He said all records - including emails, minutes of meetings, correspondence with contractors, safety assessments, specifications and reports - must be kept intact.
Mohammed, whose apartment is opposite the tower, had friends who lived in Grenfell's upper stories.
"Nothing was done to improve fire-proofing standards, The Telegraphwrites, while also citing changes in laws, unsafe cladding, no government reviews, and even missing sprinklers to try and explain the tragedy". The neighborhood's resident's association said the management company was negligent.
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The PM had earlier visited Chelsea and Westminster Hospital to meet staff and patients who were caught up in the fire. They also made a grim admission: A full accounting might be impossible because some victims may never be identified.
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