The Prime Minister met with survivors and residents of the west London tower block to discuss concerns over the handling of the aftermath of the fire, which killed more than 80 people.
Ms May admitted there were flaws in the response effort, telling residents Kensington and Chelsea Council (RBKC) “did not respond quickly enough after the fire”.
She said residents were “pleased” to hear the Kensington Tenant Management Organisation (TMO) would be removed from managing the surrounding Lancaster West estate where the tower is situated.
Lancaster West Residents Association vice chair Andrea Newton said residents wanted to see a “seamless” transition.
“We cannot face another disastrous event following the trauma we are currently dealing with,” she said.
“We will be expecting to work in partnership with our landlords on how our properties will be managed in the future.”
Leader of RBKC, Elizabeth Campbell, said she had written to the TMO seeking a “swift transition” of responsibilities to the council, and promised to consult with residents about future plans.
She said: “We wrote to the TMO yesterday and said that we didn’t think the most viable option was to work with them going forward.”
But Samia Badani, who chairs the residents association for Bramley House, a block that overlooks the tower, said there were still serious concerns for the other roughly 9,000 properties managed by the TMO in the borough.
“One thing for sure is the TMO is not fit for purpose, and we cannot forget the TMO manages more than 9,000 properties,” she said.
“There is no doubt in anybody’s mind that the TMO needs to go completely. Grenfell has showed they cannot recover from that, there have been serious failings and there has been a fundamental breach of trust.
“It seems from today’s announcement that the council has the power to restrict functions of the TMO. It’s clear we don’t want them and we don’t have faith in their ability.”
Residents have repeatedly called for the TMO to be dissolved in the two months following the tragedy, and have accused representatives of hiding from the community.
The TMO has not attended any of the public meetings held by the Government’s gold command since the fire on 14 June.
Its chief executive, Robert Black, stepped down in June in the face of growing public criticism of the organisation’s handling of the fire.
Earlier this month, his replacement, Elaine Elkington, failed to make a single reference to the tragedy in her first statement, sparking furious criticism from the local community.
“I’m looking forward to working with our resident-led board and with staff to move the organisation forward at a business-critical time and supporting our desire for continued service improvements,” she said in a statement.
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