"My heart goes out to those affected", Cundy said.
Victims made clear their demands to Mrs May in the two-and-a-half hour meeting in Number 10.
Hundreds of people descended on community centres and churches following the disaster that left at least 58 people dead, donating food, clothes and nappies while others raised nearly £3m for the victims on websites such as JustGiving.
As part of the latest action from government, a team of civil servants has been embedded into the Kensington council office.
On Saturday, NHS England said 19 people were being treated in hospital, including 10 in critical care. The emergency services expect to find no more survivors.
Anyone who has concerns about someone who they know may have been living, visiting or staying in Grenfell Towers, but has not yet been contacted by the police or not yet reported their concerns about a possible missing person should call the police Casualty Bureau on 0800 0961 233.
In a message to mark her official birthday, she said: "Today is traditionally a day of celebration".
Speaking on Friday evening, Mrs May said: "Everyone affected by this tragedy needs reassurance that the Government is there for them at this bad time - and that is what I am determined to provide".
Congressional animosity began with Newt Gingrich
On May 19, Trump nominated Gingrich's wife, Callista, to be part of his administration as ambassador to the Vatican. Nobody on Capitol Hill has any proof that I did anything with the Russians.
"I have been profoundly struck by the immediate inclination of people throughout the country to offer comfort and support to those in desperate need". "United in our sadness, we are equally determined, without fear or favor, to support all those rebuilding lives so horribly affected by injury and loss". But the shock at its scale turned to anger and recriminations on Thursday. The 24-storey tower that once housed up to 600 people in 120 apartments is now a charred ruin.
Protesters marched to the edge of the police cordon around the tower, shouting "no justice, no peace", where a few young men tried unsuccessfully to break through.
UK Prime Minister Theresa May announced a 5 million pound (6.4 million UD dollars) fund on Friday to help victims of the Grenfell Tower fire. We are not interested in your reasons for not telling us sooner, we just want to understand as best as we can who may still be inside the building'.
He said residents were "angry not simply at the poor response in the days afterwards from the council and the government, but the years of neglect from the council and successive governments".
There are questions about why the block was not fitted with sprinklers or a central smoke alarm, and whether a recent refurbishment, including new external cladding, helped fuel the flames.
The British government Sunday scrambled to contain political fallout from the London high-rise inferno that has claimed at least 58 lives as officials focused on building materials that may have spread the fire quickly.
British officials say they are helping the Syrian family of the first officially confirmed victim of the London tower blaze to come to Britain.
Friends and families of victims, including a furious seven-year-old, asked: "How many children died?"
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