They have a heavy bias towards state educated pupils.
For institutions that are supposed to contain fine minds, it's a very basic analysis to conclude:
state = poor, underprivileged, deserving of place
private = rich bastard, overprivileged, undeserving of place
The OP herself can go into either category - her child is the exact same child whichever she plumps for. Illustrating the flaw in the analysis above.
My friend's ds just got rejected. He passed the exam, had all top grades, loads of relevant preparation, experience, genuine love for the subject etc etc. Crime = going to private school. Irony = he went there because he was extraordinarily clever and got the highest possible scholarship, with no preparation, having attended a state primary.
There is a good public school near me and instead of getting several in to Oxbridge, they got 2 in. These 2 candidates were BAME, which I imagine may have negated their crime of attending public school. Not a single white kid got in. Despite one having won a national prize in their subject.
I also know someone who went to Cambridge, "salt of the earth state school pupil". Oh, but did I mention her dad is an A level examiner in the subject she got in for. Big advantage, no? But never mind, at least she isn't a "public school white boy scum of the earth" type.
I know someone else who went - daddy was a lecturer at another uni in the subject this person got in for. Mummy was a SAHM in a lovely 5 bed home making life perfect. But "state school salt of the earth". No privilege there, no not at all.
How bout the kid at the private school who had 2 dead parents and is boarding off their estate because there is nobody to look after her in a family home. Privilege? For the love of God.
It's all a load of horseshit OP and I'd send your child where you think they will fit in the best, with the school meeting their needs.