The group left after a meeting that lasted more than two hours but did not speak to reporters gathered outside.
Thirty of those have been confirmed dead while 28 others who are unaccounted for are known to have been in the building when the fire broke out.
He also said: "As the mayor of London I will do my bit to be the advocate, to be the fighter, and to be the champion of these people". Those who lost their homes will be rehoused within three weeks, she said.
Cundy said 16 bodies had so far been recovered from the tower and taken to a mortuary.
Emergency workers have reached the 24 floor, the top floor, of the tower.
Cundy promised an exhausting investigation into the tragedy. He says "my heart goes out to those affected".
"Contractor says that he met all the fire safety standards but the questions are going to be, which kind of siding was used and what were the risks?"
He said police will release images and video from inside the tower tomorrow, pending the approval of Grenfell families. A new sign was put up, removing that detail. 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".
British police release footage showing devastation inside London's Grenfell tower
Hundreds have been left homeless by the blaze, putting more pressure on officials in a city plagued by a chronic housing shortage. Around 70 people are missing, according to Britain's Press Association, and identification of the victims is proving very hard .
Major roads near the stricken building were open Saturday.
"They haven't got easy fire escapes, they've got no sprinklers, it's totally, totally unacceptable in Britain that this is allowed to happen and people lose their lives in this way".
Elsewhere, an angry protester attempted to rally the large crowd to march on the Prime Minister's residence on Downing Street. May was jeered after she made a visit to the community Friday.
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.
Labour Party leader Jeremy Corbyn said Sunday the government has the power to take over empty apartments and offer them to the hundreds of Grenfell Tower residents left homeless in Wednesday' inferno.
The queen and her husband, Prince Philip, stood silently on the steps of Buckingham Palace before the start of the Trooping the Color that each year marks the queen's official birthday, which is traditionally celebrated in June when the weather is warm. "It should define the leadership of May and she should be forced to resign", he said.
"We know that at least 30 people have died as a result of this fire".
The original Xbox 'Duke' controller is coming back
This probably won't be one of those years in which Microsoft's or Sony's showings have a big impact on how things shake out. TechCrunch says "there's no question" that the Xbox One X "is definitely a game system that puts out great visuals".
London's Metropolitan Police confirmed Friday they had launched a criminal investigation into the incident. British health authorities say that 19 patients are still being treated at four London hospitals.
Central to the anger is that cheaper materials may have been used in a multi-million dollar refurbishment of Grenfell Tower to keep costs down.
After attending a service for victims, he called the fire a national disaster requiring a national response.
Experts believe the exterior cladding, which contained insulation, helped spread the flames quickly along the outside of the tower in the June 14 blaze.
Londoners and others have also donated huge amounts of food, water and clothing, and shelter, to survivors.
British officials have announced a nationwide minute of silence to honor the victims on Monday morning.
The Grenfell Tower housed about 600 people in 120 apartments.
Jamie Lovemark on target on new US Open courses
Local health officials announced they found evidence of E. coli bacteria at a hydration station on the 12th hole on Thursday. McIlroy could at least take heart from a strong finish on Friday, which saw him birdie four of the last six holes.
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