He told ITV's Peston on Sunday that the community and emergency services were "incredible" in tackling the fire and its aftermath.
"What was less effective was the Royal Borough of Kensington and Chelsea, because they seemed to lack the resources to deal with a crisis of this magnitude in their borough and yet they are the country's wealthiest borough," the Labour leader said.
In a statement on their website the council say:
The Council is helping those affected and in need of emergency accommodation. It is also giving financial assistance to cover their immediate needs.
All residents of Grenfell Tower who have requested help have been placed in hotels.
We are now looking to source interim accommodation for those Grenfell Tower residents and also trying to assist, where possible, elderly and vulnerable residents from surrounding areas who have been unable to return to their homes due to the safety cordon.
We plan to house residents of Grenfell Tower as locally as we can.
But we may well need help from our close neighbours. We want to rehouse
people in a good home as quickly as we can. The Council is committed to
looking after the immediate and longer-term housing needs of all those
affected by the fire.
We are still placing households and housing officers are continuing to work to provide assistance and support.
The Westway Sports Centre, Crowthorne Road, W10 6RP, is now the Family and Friends Reception and is being staffed by the police.
Kensington Leisure Centre remains closed to the public as it is being used as a rest stop and staging area to support the emergency services and the local community.
We have heard a number of theories about the cause of the fire at Grenfell Tower. All of these will be thoroughly investigated as part of the formal investigation which has already begun.
Enter a name and e-mail address and we will e-mail this website link too them.