Councillors have warned Conservatives against selecting a "continuity" candidate to become the new leader of the local authority at the centre of the Grenfell Tower fire.
Daniel Moylan, Tory councillor for the Queen's Gate ward, said he understood the local Conservative group was planning to meet privately on Monday evening to discuss who they will put forward to take over from Nicholas Paget-Brown.
Mr Paget-Brown resigned on Friday after Kensington and Chelsea Council was criticised for its response to the Grenfell tragedy, in which at least 80 people died nearly three weeks ago.
Mayor of London Sadiq Khan has led calls for commissioners to be drafted in to take over the day-to-day running of affairs in the west London borough.
Mr Moylan - former deputy leader of the council - said he felt it would be "almost impossible" for someone within the cabinet to take over.
He said: "It will be fatal for the council if they choose a candidate who is capable of being presented as the continuity candidate."
He added: "On the question of commissioners, I think the council has a very short chance to sort itself out.
"I think the council should be given a chance to rebuild and regain the trust of the people."
It "has to show it is capable of doing that", he added.
Robert Atkinson, leader of the opposition Labour group, said he believed an "outsider" was needed if the council was to rebuild trust with residents.
He said: "I understand that the Tories are seeking to elect a new leader who's not contaminated by the mess. I will look very carefully to see who they select."
The councillor, who represents the ward in which Grenfell Tower is based, went on: "I have been calling for appointment of commissioners at least in the short-term.
"Very few members of the existing shambolic cabinet have a chance of getting the confidence of the people of Kensington.
"We need someone who will be empathetic to the people of Kensington".
Labour MP David Lammy, whose friend Khadija Saye died in the blaze, said: "Any prospect of new leadership from within the council ignores the fact that the positions of the council's leadership team are untenable, the local authority as a whole has singularly failed to provide the support that the Grenfell survivors and families have needed, and commissioners urgently need to be brought in to get a grip of the situation before it gets any worse".
A spokesman for Kensington and Chelsea said a council meeting would have to take place to formally elect a leader.
He said the next scheduled meeting was on July 19 but that an emergency one could be called earlier.