The letter, which first appeared in the Daily Mail, comes a day after media reports suggested that the 60-year-old Met boss had been offered to have her contract extended by two years.
"Dame Cressida Dick, who has presided over a culture of incompetence and cover-up, must not have her contract extended and must be properly investigated for her conduct," it read.
Met critics, who include the mother of a black teen Stephen Lawrence who was slain by a group of white youths in 1993, said Dick should be replaced by someone outside of London through a "truly independent and transparent process."
The letter insisted that Dick’s predecessors and appointees also had questions to answer and urged the "demonstrably unfit for purpose" police watchdog IOPC to be reformed so that it could properly investigate complaints against the police.