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.
Brooks Koepka wins US Open title
Jordan Spieth may not have finished in the top either, but he had one of the best rounds Sunday at -3. Fowler gave himself a break: "You kind of have to say, 'Hey, it's a major, I played well this week"'.
Koepka wins US Open title
In fact he made a mad rush to the finish, birding 11, 12, 14, 16 and 18 to enter the clubhouse only a shot back. That merely added to the drama, though, as a crowded field sorted itself out in a taut U.S.
Portugal held by Mexico at Confed Cup
The team from CONCACAF had enjoyed nearly 70 percent of possession against the European champions, but hadn't threatened the goal. If the game was a test of those factors, Mexico passed. "We nearly had the game won but we suffered in the final minutes".
Fleetwood: 'Pictured winning the US Open a lot'
Rory McIlroy of Northern Ireland reacts after finishing on the ninth green during the second round of the 2017 US Open . Opens, Johnson added life to what is traditionally golf's toughest and often most drama-free major.
Mueller Has 'Not Yet' Decided to Investigate Trump
Trump got rid of Comey, in May to hamper an inquiry into his sacked national security adviser, Michael Flynn. If Trump would seriously consider firing Sessions, it stands to reason that he would dispose of Comey.
Confed Cup: Portugal draw 2-2 with Mexico
And on the video referral system ( Portugal had a goal ruled out for offside by the video assistant referee): "It's the new rule". Having threatened with a header earlier, Hernandez stole in to head home an equaliser three minutes from the interval.
Microsoft unveiled its new console, Xbox One X
Do you think PS4 Pro is a Xbox One competitor? Xbox One X will debut on November 7 for $499 Dollars . The backwards compatibility program is expected to launch later this year with a couple more titles.
Pakistan make history, win Champions Trophy
Chasing the target of 339 India were all out in 31st over. "We played very well and know we have won the final", Ahmed said. India won the toss and chose to field first in the Champions Trophy final at The Oval.