May made the announcement while speaking to survivors of the fire that on Wednesday ripped through the 24-story Grenfell Tower in Kensington while most residents were sleeping, leaving dozens dead, of which 30 have been found and identified, and hundreds homeless.
Cundy said there may have been other people in the tower that police are not aware of, which would add to the final death toll.
"Afterwards, she will meet a group of residents, victims, volunteers and community leaders in Number 10".More news: White House Confirms Trump's Speech on Cuba in Miami on Friday
Mrs May has since visited survivors in the Royal Kensington and Chelsea Hospital as well as meeting residents at a church in Kensington on Friday, where crowds pelted her with cries of "shame on you" as she left.
The fire has been a major test for Prime Minister Theresa May, whose Conservative Party is clinging to power after losing majority control of Parliament to a Labour surge in a snap election this month.
Mrs May has promised a public inquiry into the catastrophe, and also pledged £5 million (Dh23.5m) of support, housing guarantees and help with access to bank accounts and cash.
"We are ensuring that within three weeks people will be rehoused so that they have a home to go to".
The building was run by Kensington and Chelsea Tenant Management Organisation (KCTMO) on behalf of Kensington and Chelsea London Borough Council.More news: Benfica star Talisca admits Manchester United move is his dream
"Absolutely she has the same degree of sympathy and horror at these events that we all have", he added.
"I would like to ask anyone who was in Grenfell Tower that night, but for whatever reason has not told us they are safe to please call our Casualty Bureau".
She said earlier that the national mood is somber but that Britain is resolute in the face of adversity. "We need answers and we need answers now", another man said through a megaphone.
The area surrounding the tower has been plastered by desperate relatives with pictures of the missing, from grandparents to young children. "The country has witnessed a succession of awful tragedies". Earlier in the day, the 91-year-old monarch described the country's mood as "somber" but insisted that Britain remained resolute during a hard time. "Put to the test, the United Kingdom has been resolute in the face of adversity. Wherever we can, we will bring people to justice if there is evidence". He said he was "heartbroken by the tragic fire and the appalling loss of life".More news: Russia coach has comic touch at Confederations Cup
The block, which housed some 600 people in about 120 apartments, is in a low-rent housing estate next to one of the most affluent areas of Britain. But the meeting is unlikely to quell complaints that the prime minister has been slow to reach out to fire survivors.
- Trump Says FAA "Didn't Know What the Hell They Were Doing".
- New Analyst Ratings For Big Yellow Group (LON:BYG)
- Defending champion Johnson out of US Open
- Portuguese radio says 25 people killed in forest fires
- Kershaw wins, Bellinger hits 2 homers as Dodgers top Indians
- Tributes as Germany's Helmut Kohl dies, aged 87
- Obamas invited to be honorary football coach at University of MI
- UK Government 'absolutely steadfast' in commitment to peace process - Theresa May
- Brexit talks with European Commission to begin on Monday
- Celtic complete signing of Johnny Hayes