Police received report of the fire at the building at 1:16 a.m. local time (0016 GMT).
"Our absolute priority for all of us is identifying and locating those people who are still missing", Cundy said before declining to comment on speculation about the likely final death toll: "It would be wrong for me to get into numbers that I do not believe are accurate".
17 people have been confirmed as dead following the devastating blaze - but dozens are thought to have died, with fears the figure could reach more than 100 people.
Ambulance officials said that 78 people were receiving medical treatment in hospitals, with 18 of those patients in critical care.
There is no evidence that that the fire was a result of a terrorist activity, the police representative added. Daffarn said residents had complained for years to London City Council about building safety, to no avail.
The public housing block of 120 apartments was built in 1974 and recently upgraded at a cost of 8.6 million pounds, with work finishing in May 2016, according to the Royal Borough of Kensington and Chelsea.
Thomas, who will also feature in the line-up, said that organising the fundraiser is "the least we can do to help our fellow Londoners". While the death toll remains unclear, the BBC reported Thursday, citing anonymous sources, that as many as 100 people may have lost their lives in the blaze.
Fire Commissioner Dany Cotton says specialist dogs would start searching the 24-story building.
Prime Minister Theresa May, who has promised an investigation into the disaster, visited the scene on Thursday to meet members of the emergency services, but left without making any public comment.
The fire engulfed a 24-storey building in west London in the early hours of Wednesday. Survivors told of frantic attempts to escape during the nighttime fire. "She said she felt like she was going to faint". She said early Thursday that authorities had finally extinguished the last pockets of flame, and were trying to secure the edges of the building for a fingertip search. But the focus has turned to renovations completed a year ago that added decorative touches to the building.
Missing people posters have been put up throughout North Kensington.
TV chef Jamie Oliver offered victims food and drink free of charge at his restaurant in the nearby area of Shepherd's Bush, while British presenter Jeremy Clarkson cleared out his wardrobe to find clothes to donate to those affected, urging others to do the same.
He also sympathized with families of the victims who lost their lives during the incident.