It deeply depresses me that our esteemed Education minister cannot see that the major, defining difference between state and private is Selection. And I don't mean grammars: even they had to adhere to the same policies as yer bog-standard comp, at least on paper, when it comes to chucking out the feckless, disruptive, uninterested, and yes, bothersome, expensive SEN. If every school in the land were allowed to select its intake, the quality of its output would rise.
Simples.
As for class size, it's my belief that a lot of academic private schools have class sizes of 25 odd; but those 25 are of very similar higher ability (academic selection); MC or 'higher' (selection by wealth); and committed (selection by very focuses parental input).
As an aside, I always 'smile' when I hear outrage that a 'good school' isn't being allowed to massively expand so that more DC can go there as I privately think 'well, the reason that school is considered to be 'good' is because it is what it is, chuck in a wider cohort of DC, i.e. selcet more using wider criteria and suddenly you might find those magic standards falling'.