It's understood Dame Cressida Dick submitted a plan for reforming the force after facing criticism following a series of scandals, including the murder of Sarah Everard by a serving officer.
Head of policing for South-West London, Lis Chapple, says "We are losing a committed public servant, a wonderfully positive role model and a clever, thoughtful, values-led leader".
Kingston MP and Lib Dem leader Sir Ed Davey has been calling for her resignation since the alleged mishandling of the vigil for Sarah Everard on Clapham Common.
He says Boris Johnson must have no role in choosing her successor, since he’s currently being investigated by the Met.
But London Mayor, Sadiq Khan, says he "wasn't satisfied" with her plans to root out racism, sexism, homophobia, bullying, discrimination and misogyny.