"by the time A levels are being studied those not interested in the subject have opted put. You're left with a self-selecting cohort who've chosen to be there."
Not entirely true... at the moment at least, we do get students on our courses because they're there for their EMA. In fact on one of my courses that started in Jan, not one student was there because of a desire to actually do the subject, they were all there to make up their timetables, get EMA etc etc...
Also, having taught in both the state and the private sector, I think there are some students who are naturally bright who would get an A wherever they studied, state or private.
However, they are also those students who will scrape their As with a lot of support, and given that private schools can often afford to give more support than state schools, then it will be easier to achieve in private schools.
My friend taught in a private school, and she actually had written into her contract that she was given an average of half an hour per student per week to provide 1:1 tuition for those who needed it. Where I teach now (state) I have about half an hour per half term. Therefore, any extra support the students need either comes out of my free time (as it usually does) or the student goes without.
Another public school near me regularly pays for the chief examiners of the subject to go and talk to students, to give them guidance on how to answer their exams and tips etc. We can never provide anything like this. I've been to one of these sessions - and what the students got from it, was amazing.
Incidentally, I run a weekly support session for my students (I don't get paid for this) to help them in any way they need. I would say that I see more students who are wanting to boost their grades from a B to an A than I do at the bottom end of the spectrum. Interestingly, my value added scores are really high year on year, and it has a really positive effect. When I taught in a private school, it was standard to offer this and teachers were paid for doing so.
Finally, whilst I'm sure this has already been mentioned, but when I taught private I had 8 in a class. Now I've got 24 in one of my A2 classes. It makes a big difference.
Whilst teachers are the same from state to private are the same (I've taught both!), the facilities and support differ widely.