The Kensington and Chelsea Conservative group has chosen Elizabeth Campbell as its new leader.
Nicholas Paget-Brown remains leader of the council for the time being but Ms Campbell becomes de facto leader.
It is expected that she will be confirmed as leader of the council at its next full meeting on 19 July.
Mr Paget-Brown resigned on 30 June following continued criticism of the council’s handling of the Grenfell Tower tragedy.
In her first statement since her selection, Ms Campbell said: “The first thing I want to do is I want to apologise.
“This is our community and we have failed it when people needed us the most. So, no buts, no ifs, no excuses.
“I am truly sorry.”
She said as the new leader she would appoint a new cabinet on Tuesday and vowed, “things are going to change”.
Her first action would be to reach out to the community so that wounds could begin to heal, she added.
He second action would be to call Sajid Javid, secretary of state for business, to ask for more help.
She said she was unsure at this stage exactly what form that help should take but said she needed to draw up a plan for north Kensington.
The Conservative group control 40 out of 50 seats on Kensington and Chelsea Council.
Ms Campbell has been a councillor in the borough since 2006 and represented the Royal Hospital Ward since 2010. She was previously a Conservative parliamentary party candidate in for Gateshead East in 2001
Local politicians have warned the new leader must come from outside the “contaminated” administration.
Councillor Daniel Moylan said the ruling Conservative group has to “show a complete break with the past”.
Mr Moyland, the Conservative former deputy leader of Kensington and Chelsea Council, said “any idea of a continuity candidate would be a very bad idea”.
“We have to be able to go to the people of North Kensington and to the victims of the fire with a real sense of acknowledging how badly they have been let down, a real sense of shame if you like,” he told BBC London Radio.
Judith Blakeman, a Labour councillor in the ward which houses Grenfell Tower, said “it can’t possibly be one of the cabinet members” as they had voted to endorse the former leadership.
“They are all contaminated. No member of the current cabinet would have any credibility with the residents of North Kensington,” she added.
Sadiq Khan has called for commissioners to take over the running of Kensington and Chelsea Council.
The Mayor of London said the government had “no option” but to appoint “untainted” commissioners.