Carrick, who was given 37 life sentences for his crimes, was not properly vetted in 2017, with checks failing to reveal an allegation of domestic abuse against him.
Mitchell was allowed to join the force in 2020 after a vetting panel, which partly aimed to improve diversity, overturned a decision to reject him from the police despite a previous accusation of raping a child.
The review published on Thursday found that thousands of police officers and staff were not properly checked amid pressure during a national recruitment drive from July 2019 to March 2023.
Senior officers at the Met chose not to meet national guidelines amid a scramble to find more than 4,500 recruits.
The deviations from standard practice meant thousands of references were not checked, and shortcuts in vetting led to there being some officers and staff who should not have been in the force. This contributed to “police-perpetrated harm” and damaged public trust, the review said.
Under the Police Uplift Programme, forces in England and Wales were expected to recruit 20,000 officers within three and a half years to replace those cut during austerity, and funding was ringfenced and lost if targets were not met.