"We have had so much support for the local community and we can not thank everyone enough", King said.
Addressing the Commons on Wednesday, the Prime Minister said the initial support on the ground for families was "not good enough" with people lacking basic information about what they should do and where help was available.
"We opened the door to her and she took her sunglasses off and said: 'Hi, I'm Adele, '" he recalled.
Demonstrators march in central London, many demanding justice justice for the victims of the recent deadly apartment block fire at Grenfell Tower, as they march towards parliament in central London Wednesday June 21, 2017.
The 68 one, two and three bed flats have been bought by the City of London Corporation in response to the tragedy and handed to Kensington and Chelsea Borough Council for "long term" social housing.
John Barradell, head of the newly established Grenfell Fire Response Team (GFRT), admitted that even a week after the blaze, the effort still needed to be stepped up to help victims.
"First, landlords of high-rise residential buildings should review and urgently reissue fire safety advice to residents and those at the meeting agreed to do so".
Since the tragedy, the Government announced it was triggering a £5 million emergency aid fund to help those affected.
While the affordable housing won't be as luxurious as those for private sale, the news release states that "each home will be fully furnished and completed to a high specification". "Properties must be found, requisitioned if necessary, to make sure those residents do get rehoused locally", Corbyn said.