I'd add Hampstead and Highgate to Stut's list. They're on ether side of Hampstead Heath (700 acres of park) and they have underground stations. Richmond also has a lot of green parkland, and railway lines into the centre, so that might also work.
If you want quiet AND central (that requires a different definition of quiet, I guess) then Bloomsbury might work, as AlwaysFlyStar suggested. You could add Primrose Hill and Notting Hill to that list. They're not "quiet" in the same way that Stut's recommendations are quiet, but that's where to look for some oases of calm amid the madness that is London.
EDIT - And to Stut's list, you could add Dulwich and Greenwich. All the Wiches and Hills ...