These are stats for 2019 (didn't bother with 2020 as it probably wasn't a representative year). Overall, 8,470 applications from the 'home maintained sector', but within that -
Comps - 4,642 applied - 1,219 offers
Grammars - 2,121 applied - 728 offers
(plus the stats for sixth form colleges and FE colleges)
Then for Independents - 3,295 applied - 999 offers
So on the face of it (my maths is terrible so can't work it out exactly) - around a third of grammar school and independent candidates received offers (roughly); whereas for comps the ratio was slightly lower? The ratio for FE colleges lower still?
But anyway, this table shows the different offer ratios for the different types of schools within the 'home maintained sector' with grammar schools as a distinct group. No academies.
I think it's worth looking at offer ratios rather than actual admission rates because O and C can only make offers - they can't control whether a student actually goes in to get the grades.