Cundy, speaking outside Notting Hill Methodist Church, confirmed the previous death toll of 30 but said 28 more people likely died in the fire at the 24-story apartment building on Wednesday.
Authorities in London said Saturday that 58 people missing are presumed dead from this week's fire disaster at a high-rise tower.
Cundy added that the figure could change.
Following the two-and-a-half-hour meeting, a spokesperson confirmed that a series of demands and expectations had been established and said the group would make a full statement on the meeting once it had returned to the community.
British Prime Minister Theresa May on Saturday met with victims of the Grenfell Tower fire at 10 Downing Street a day after protesters criticised her for visiting and leaving the scene on Thursday without talking to any of those who had lost their homes in the blaze.
"Nowadays, we would not dream of building towers to the standards of the 1970s, but their inhabitants still have to live with that legacy. 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", May said as quoted by the Financial Times newspaper.
But on Friday she continued to sidestep questions over whether she had failed to grasp the mood of the public by failing to meet with residents in the fire's immediate aftermath.
He told the Press Association: "I'm positive because I think it was a real chance for local residents, people affected by this tragedy, to voice their concerns directly to the Prime Minister so that she could hear them".
"Government is making money available, we're ensuring that we're going to get to the bottom of what's happened, we will ensure that people are rehoused. Again, I would urge them if that is you, I don't care the reason, please, please contact us".
May on Saturday chaired a meeting on the government's response to the fire.
"At least she could've met the victims, [Labour leader Jeremy] Corbyn was a good man. he came and met the people", one victim told Sky News.More news: Pakistan's Amir fit for Champions Trophy final
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Cundy said police would consider criminal prosecutions if there is evidence of wrongdoing and the police investigation would include scrutiny of the renovation project.
This, however, is only a quibble; even if Grenfell Tower could not have been saved, there are surely other buildings where fires will soon occur that would benefit from sprinklers.
She has promised to set up a public inquiry and pledged 5 million pounds ($6.39 million) of support, housing guarantees and help with access to bank accounts and cash.
A Downing Street spokesman said the PM had "sent her best wishes" to the Queen, who has marked her 91st birthday with a sombre but defiant message. "If more funding is required, it will be provided", May said, while more than 1,000 protesters rallied outside her residence Saturday.
"The Prime Minister is distraught about what has happened", said Green, who was appointed May's deputy in the wake of the general election. Of course, this disappoints me as I gave an assurance on behalf of the Government at the time, based on the advice of officials that we would do this. "This year, however, it is hard to escape a very somber national mood".
"The fire at Grenfell Tower was an unimaginable tragedy for the community, and for our country".
"Put to the test, the United Kingdom has been resolute in the face of adversity", she added. "United in our sadness, we are equally determined, without fear or favour, to support all those rebuilding lives so horribly affected by injury and loss".
Firefighters at the Grenfell Tower block which was destroyed in a disastrous fire in London on June 16.
Her failure to win a majority in an election that she did not need to call had already sparked a tumultuous week and pitched Britain into its deepest political crisis since the Brexit referendum a year ago.
Some 19 patients are still being treated in hospital, of whom 10 are in a critical condition, the National Health Service said Saturday.