PaddyFodder - also Oxbridge and all unis these days make “contextual offers” - eg DS is required to achieve A*AA for a particular course, the contextual offer for students in state schools (not high performing grammars etc) is AAB.
As for the disproportionate amount of students coming from independent schools, the fact is, private schools vary A LOT. You could argue it’s harder, relatively speaking, to get into some of the super-selective independents in London, where ten children apply for every place at 11+, than it is to get onto certain courses at Oxbridge where the ratio might be three applicants for every place. So it’s not surprising that certain schools will be sending 20% to Oxbridge, given how selective they are in the first place. Look at the GCSE results, 95% 9-7 grades at GCSE etc. They don’t claim to represent the national range of abilities, do it’s not comparing like with like. They will also be sending that number again to Ivy League or other equally competitive unis such as Imperial, UCL or LSE, etc.
There will obviously be other private schools that cater for SEN or non-selective ones, particularly once you get into less populated or rural areas.
It doesn’t matter where you are coming from, a “thicko” as you call him / her will not get into Oxbridge regardless of where they’re coming from. Those days are long gone. Getting AAA is hard from any school and nobody does the exams for them.
Though it is true, of course, that schools which see Oxbridge as perfectly attainable are likely to inspire more students to feel as if they can have a go.