Cundy also said the London Fire Brigade searched "every floor of the building" and recovered 16 bodies, but added it may take weeks for the search and recovery operation to become "significant".
Cundy said there may have been other people in the tower who police are not aware of, and that could increase the death toll.
On Saturday afternoon, victims of the tower block fire - along with volunteers and community leaders - met with the Prime Minister at Downing Street.
Ms May was criticised for avoiding locals when she visited the charred shell of the 24-storey tower on Thursday and faced cries of "Shame on you" and "coward" when she returned on Friday.
"But, frankly, the support on the ground for families who needed help or basic information in the initial hours after this appalling disaster was not good enough". The Independent reports that Saye posted to Facebook at 3 am Wednesday that she and her mother were trapped in their apartment, and asked people to pray for them.
On Saturday afternoon 58 people were confirmed to be missing, presumed dead.
"I have been profoundly struck by the immediate inclination of people throughout the country to offer comfort and support to those in desperate need".
Mrs May, already under pressure after a botched snap election, is facing widespread criticism for her response to the blaze.
Told there was a need for the public to hear her say something had gone badly wrong and the Government accepted responsibility, Mrs May said: "Something bad has happened".
He also said survivors from the tower would be re-housed in the local area.
The government has promised a full public inquiry, but that has done little to a sense of frustration and anger among residents and neighbours who demand answers for how the blaze spread so quickly and trapped so numerous tower's roughly 600 residents.
On Saturday night, the Government announced new measures to support those who have lost loved ones, along with members of the emergency services.
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.
"I want to know and we all want to know that you are safe and well".
London Mayor Sadiq Khan wrote to May on Friday, saying residents felt increasingly enraged and frustrated by the slow response from the authorities.
Queen Elizabeth, 91, and her grandson Prince William also visited residents and emergency workers on Friday.
She eventually met with residents of the Latimer Road fire, thought Jeremy Corbyn and the Queen were on the scene before her.
Cundy said it could take a number of weeks to complete the search of the tower.
Londonpolice said an investigation, led by a detective from its homicide and major crime unit, would examine whether criminal offences had been committed although they said there was nothing to suggest the fire was started deliberately.
"We're all desperately sad, we're all angry, but of course none of us as angry as those who were directly affected".
Una potenza da non sottovalutare per una macchina di questa gamma, da accoppiare ad una guidabilità invidiabile. Da non sottovalutare anche il "Display Audio" da accoppiare (se richiesto) al sistema di navigazione.
Mr Kenny made his final speech to the Dáil on Tuesday, stating that he had always strived to get the best for the Irish people. Questions already loom over how long the new Taoiseach - Ireland's 13th - can hold on to the office.
Scalise, 51, was in dire condition when he was first shot, but internal bleeding is under control and the prognosis is positive. Saclise's doctor, Jack Sava, said Scalise will need further operations but he is expected to be able to walk and run again.
The Warriors are headed to San Francisco, where they broke ground this year on a new arena slated to open in 2019. The Golden State Warriors celebrate during the Warriors 2017 championship victory parade in downtown Oakland.
Police said that Junaid Mattoo is the third top militant who has been killed after Burhan Wani since past year . Mattoo , a notorious militant was LeT district commander and took part in a number of militant activities.
Rosenstein on Thursday night issued an unusual and puzzling public warning about stories attributed to anonymous sources. Rosenstein also appointed Robert Mueller to investigate ties between Trump's campaign and Russian Federation .
Stockbroker and CNBC personality Josh Brown tweeted that the Warriors would skip the White House visit, citing "reports". Several Warriors players and coaches have been outspoken in their criticism of President Donald Trump this season.
There is a sense, from conversations with locals, that people have had enough with the VIP visits, even when it is the Queen. Mohammad Al-Hajali, 23, a refugee who fled Syria for the United Kingdom in 2014, was identified as another victim.
It was a matter of time for India to emerge victorious yet again against their nemesis Pakistan and register a 124 runs win. This was a view endorsed by Kohli during his pre-match press conference at Birmingham's Edgbaston ground on Saturday.
Durant's 11 points and Golden State's attacking defensive work powered the surge. "I think we'll do it again next year". That's what we needed. "But we were able to keep our eyes open to someone who could make this whole thing complete".
Warriors Green makes fun of Cavaliers
Whether Curry decides to attend or not, the result and achievement stays the same - he is an NBA Finals champion. It ended the way many believed it would when Durant signed a free agent contract with the Warriors last summer.
Uber CEO Taking 'Undetermined' Leave From the Company
This follows recommendations made by former U.S. attorney general Eric Holder for a shake-up of the company's workplace practices. He said his "beliefs and approach to leadership" were "inconsistent" with those of the company.
58 presumed dead in London tower fire
The official death toll confirmed by authorities stands at 30, with around 70 people missing. Some residents had warned months ago that the tower represented a unsafe fire risk.
Warriors celebrate NBA title with parade through Oakland
May 30, 2016 - Western Conference Finals - The Golden State Warriors defeat the Oklahoma City Thunder with a series win, 4-3. As revealed on the Warriors' website , the 2017 Warriors Championship Parade will commence on Thursday, June 15 at 10 a.m.
Another Victory Parade for the Warriors
So, I'll have that mindset, KD's going to have that mindset". "Oakland represents all of us", Kerr told KTVU. And he said, "I'm just not - I just wasn't focused", he said.
Shooter went to GOP baseball practice with list of names
Scalise had been awake immediately after the shooting, Sava said, but had gone into shock by the time he arrived at the hospital. Bailey was spotted Friday in the Capitol, on crutches and out of uniform, accepting congratulations from fellow officers.
Trump cries witch hunt amid Russian Federation probe
Donald Trump calls the Washington Post report that he was under investigation the single greatest witch hunt is U.S. history. Mr Trump denied those allegations, saying he would be more than willing to offer his own testimony under oath .
Andy Murray battles past Juan Martin Del Potro
But under a cloud-filled sky at Court Philippe Chatrier, Murray was looking more and more like the top-ranked player that he is. Carina Witthoeft turned up late for her third round match against second-seeded Karolina Pliskova at the French Open .
Minnesota officer acquitted in shooting of Philando Castile
Prosecutor John Choi, who made the decision to charge Yanez, said although he was disappointed, the verdict "must be respected". The immediate aftermath of Castile's shooting was captured on video recorded by Reynolds and broadcast on Facebook Live.
Rodman returns from "really good" North Korea trip
American student Otto Warmbier , center, is escorted at the Supreme Court in Pyongyang, North Korea, Wednesday, March 16, 2016. US President Donald Trump has made "solving" the peninsula's problem a top priority for his administration.
Stars want to keep Warriors together
People aren't going quite that far just yet. "I ain't doing no slaying". "We played like we did", Durant replies with a smile. James' legacy as a Hall of Famer is surely already secure but aged 32 his window on a fourth Championship may be closing.
Ryan: "Let Mueller do his job"
He added, "I think the best vindication for the president is to let this investigation to go on independently and thoroughly". Lawyer Jay Sekulow, a member of Mr Trump's legal team, has also refused to rule out Mr Mueller's possible sacking.
Democrats win annual baseball game with special meaning
Earlier today, Congressman Steve Scalise underwent a second surgery related to his internal injuries and a broken bone in his leg. Scalise and the others had been at the GOP team's baseball practice in nearby Alexandria, Virginia, when they were shot.