The Government has rejected calls for commissioners to run Kensington & Chelsea RLBC after it was blamed for mishandling the response to the Grenfell Tower fire.
London mayor Sadiq Khan had asked prime minister Theresa May to intervene because he said the council had 'lost the trust of local residents'.
Cllr Elizabeth Campbell is expected to be the council's new leader and used her first interview to apologise to the local community for the way the tragedy had been handled and to explain that she would ask Whitehall for further help.
Council leader Nick Paget-Brown resigned on Friday, accepting responsibility for the 'perceived failings' of the authority.
In a resignation statement, he said: 'The scale of this tragedy was always going to mean that one borough alone would never have sufficient resources to respond to all the needs of the survivors – and those made homeless – on its own.
'We have been very lucky to have the support of other London boroughs, the emergency services and the community associations based in north Kensington and I am very grateful to all of them.
'The task for my successor is to ensure that the strengths which also characterise this place, and north Kensington in particular, are seen to play their part in bringing the community together and ensuring that this borough, the most wonderful place, can start to move forward from this tragedy.'
Deputy leader, Rock Feilding-Mellen, also resigned.
'I will continue to serve the residents of the borough as best I can as a councillor and I will of course co-operate in full with the public inquiry.'
But Mayor Khan argued that all members of the council were tainted by its response to the disaster.
Fire survivors and neighborhood residents have accused officials of ineptitude and a lack of concern for their plight.
Mayor Khan said: 'It is crucial that the commissioners are people of high standing and probity, have a genuine empathy for local people and the situation they face and be untainted so that all residents of Kensington and Chelsea can have confidence in them.'
But communities secretary Sajid Javid said now was not the time for central government to get directly involved.
He said: 'We will be keeping a close eye on the situation.
'If we need to take further action, we won't hesitate to do so.'
Local Government Association chairman Lord Porter has stopped short of calling for the Government to send in commissioners to the council but did not rule out the idea when questioned.
The Department for Communities and Local Government has yet to comment on whether it is considering intervening.
Cllr Paget-Brown, who had resisted calls to quit in the two weeks since the blaze, stepped aside after Ms May criticised him for abandoning a meeting on the fire because journalists were present.
He initially sought to bar journalists, then scrapped the session after media groups won an injunction allowing reporters to be present.
Cllr Paget-Brown said the presence of the media would 'prejudice' a public inquiry into the disaster.
Giving notice of the meeting, the council said it would be ‘held entirely in private session in the light of the risk of disruption (as witnessed on Friday 16 June) and consequent security and public safety concerns’.
The notice continued: ‘As such, it will be open only to council members, support officers and invited guests (if any).
‘Under common law and statute, the chairman of a meeting has the power to exclude the public if he or she is of the opinion that there shall be a disruption to the business.
‘It is also lawful to exclude the public before a meeting if there are grounds upon which to anticipate a disruption of the proceedings.’
A council spokeswoman said it had taken the same approach towards journalists.
A statement read: 'As you are aware there have been recent real threats and assaults on council staff and damage to one of the office buildings.
'Such risks remain and we have had to take the decision to hold the meeting in private as to do otherwise would likely result in disorder.
'The decision to exclude the public in advance is in accordance with the council’s standing orders, which are confirmed in common law.'
The spokeswoman added that the minutes of the meeting would be published 'as soon as possible following the meeting' and that the authority would hold a full council meeting next month that would be 'open to all'.
One Grenfell resident told Sky News: 'I think they all need to resign.
'If they really want to see if they have the support of the local community, they should immediately force by-elections in all of their wards.'
Cllr Paget-Brown announced on 30 June that he would step down once a new leader was in place, but he will remain as a councillor.