@tadger98 ..
You are looking at this from one point of view.. there is another..
All children are born equal in the eyes of 'the creator'... but those that go through fee paying schools have a much higher chance of ending up at University, especially the top 10.
Those factors include genetics, family income, ethnicity, neighbourhood and school environment.
'Controlling for' X or Y factors does not control for all factors many of which are independent.
The 7% versus 18% sweeps aside the fact that the difference in those percentages is not accounted for by greater numbers of students being educated privately for A levels, but the fact that fewer students aged 18 do A levels. The 18% statistic is no longer as widely quoted since it has been pointed out that it is the denominator that changes to reach this higher percentage, not the numerator.
The fact are that fee paying schools get a greater share of top grades than non fee paying schools... again, many factors at play but not all down to selection as there is selection involved in the progression to Sixth form college and earlier at grammar scholl selection where those are in existence.
I am not going tp draw parallels in this post (though I am doing so in my head!) ... but the insistence that fee payers have a greater right to a disproportionate share (7%) university places is one position to take, the other is that every child should have an equal right to a place and that the selection processes should take all factors into account.
Neither of these positions are entirely valid or entirely possible to implement.
There is a desire among certain quarters to redress the balance, to correct for structural disadvantages in our society and to increase representation of all parts of our society amongst those who will be designing and shaping our future society and that widening access to university is a vehicle to do so.
Whether you agree with it or not...