choux, the mayor can tell the commissioner what to do, but can't do anything about it if he/she fails to do it. Hiring and sacking is the job of the central government. I suspect she's been shamed into stepping down; alternatively, there may be a peerage on the way, but it'll be none of Khan's doing.
About all the London mayor is responsible for is transport.
Khan told Dick last week that he was unhappy with her performance, but I doubt it was that little push that made her go.
Priti Patel has been getting lots of ear ache from Conservative MPs, I reckon Patel has had enough and told her to go.
Gromit, from the BBC link:
'Damaged confidence'
She said in a written statement: "It is with huge sadness that following contact with the mayor of London today, it is clear that the mayor no longer has sufficient confidence in my leadership to continue.
"He has left me no choice but to step aside as commissioner of the Metropolitan Police Service."
Prior to a claim for constructive dismissal perhaps?
if you recollect the Mayor of London said on election I can work with X and X resigned a few mins later
and a few months later collected six figures for constructive dismissal
and that Mayor of London boys and girls you know as one Boris Johnson
cant remember the now very rich Mr X
[ I love it when Abers maunder 'wot all dat mean den! - maunder on proles! ]