It came after the shadow home secretary accused Ms Patel of having been “silent on policing for a year”, during which time urgent reforms had been needed.
Yvette Cooper told the BBC she was “concerned” that the debate was “focusing on one individual, one individual new appointment, and also one police force”, adding that the policing challenges were “much broader” and required Home Office-led changes.
“Crime is going up, prosecutions are going down and confidence is falling,” she warned.
Police training, vetting, misconduct, internal culture issues, and ensuring the safety of women and girls were among the areas for improvement cited by Ms Cooper.
Her intervention followed warnings from a former HM Inspector of Constabulary that the “real cultural” problems in the force could not be fixed overnight.
Zoe Billingham told Sky News: “Whoever the incoming Commissioner is, they will have a very, very full inbox. They will have precisely the same problems that Cressida was contending with.”
She said in defence of Dame Cressida that she had “care, compassion and candour” and “really generated great loyalty amongst the frontline troops” but was overtaken by “catastrophic events”.
Dame Cressida’s exit comes in the wake of an onslaught of criticism of the force, including over its handling of the case of Sarah Everard, who was murdered by Wayne Couzens, a serving Met Police officer.
Controversy has also beset the force over its handling of alleged lockdown-breaching parties in Downing Street and Whitehall, as well as a police watchdog’s recent exposure of violently racist, misogynistic and homophobic messages exchanged by officers based at Charing Cross police station in central London.