Nick Paget-Brown, head of the Kensington and Chelsea Council, had come under increasing pressure to step down since Thursday evening, when he adjourned a council meeting held to discuss the fir at Grenfell Tower.
Announcing his resignation, the council leader said he had to accept responsibility for "perceived failings" by the council after the tragedy.
"I have therefore decided to step down as leader of the council as soon as a successor is in place," he said.
The council's cabinet had adjourned yesterday's meeting in an attempt to ban members of the public and press, claiming it would "prejudice" the ongoing public inquiry into the west London fire.
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"In particular, my decision to accept legal advice that I should not compromise the public inquiry by having an open discussion in public yesterday has itself become a political story. And it cannot be right that this should have become the focus of attention when so many are dead or still unaccounted for," Paget-Brown added in his resignation statement.
A Number 10 Downing Street spokesperson said: "The High Court ruled that the meeting should be open and we would have expected the council to respect that".
Paget-Brown faced repeated calls to step down, both from political opponents and groups representing Grenfell Tower survivors and relatives.
His resignation was welcomed by the London Mayor, Sadiq Khan, who branded the council "not fit for purpose".
"Last night's decision to abandon the council's cabinet meeting has merely compounded the misery for local people who are grieving, traumatised and desperate for answers," Khan said.
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