David Holdsworth, the registrar and chief operating officer at the Charity Commission, which has been helping to coordinate the efforts of various groups collecting aid, said the victims now had “a clear and simple way to access the funds,” but he acknowledged that some had not yet done so, perhaps because they were still suffering shock and grief.

“We are now seeing an increase in applications for charity funds, and we expect that to continue and for dispersals to those affected to continue to increase,” he said.

Questions about the speed and effectiveness of the response by charities came after widespread complaints about the lackluster and uneven performance of the local government, the Kensington and Chelsea Borough Council.

Shortly after the fire, the central government stripped the council, which owns the building, of its power over the response, and several council officials have resigned. The foundation, which works with the council but is independent of it, said that the organization had faced delays in its effort to ensure that the money was reaching the right people.

“Further cash grants are being processed, and all of the funds raised will go to the families and community that has been affected,” it said in a statement.