@BilberryBaggins
I don't think it is handicapping people in other cohorts; if you look at an independent school for example, if you didn't think it was beneficial to go there (ie if it wasn't conferring advantage by being in that school), then you wouldn't pay the fees.
With grammar schools it's a bit more complex, because it depends on your local set-up, but you still have the phenomenon where in a school where a much smaller proportion of the cohort achieve high grades, it is harder to personally buck the trend and reach those levels. For example if you are in a school with no 6th form, you may have fewer specialist teachers, because there is an incentive for specialist teachers to want to teach A level.
When you look at the actual make up of Oxbridge cohorts, it's clear that any and all of these contextual aspects do not really prejudice against students in grammar and independent schools.
I think the GCSE CAGs of last year threw up some interesting comparisons. Until recently I worked in a poor-performing secondary school (not on the teaching side but as anyone knows who works as support staff in schools you still get to hear all the political stuff that goes on). My own children go to the only grammar in our city. My kids' school seemed to grade "harshly", whereas let's just say there were some VERY surprising high results coming out of the comp

. There were rumours (that I can well believe) that when a member of SLT was given the grades by the HODs to oversee & sign off, that there was a bit of a blanket "oh, let's err on the side of caution and put them at the higher grade". Had some of the HODs had to provide evidence for those grades they probably would have struggled to do so, but the grades stood. It was a punt, and it paid off.
At my kids' grammar, just from talking to other parents and hearing what DS told me (and being surprised at one of his grades, lower than expected), a lot of the kids seemed to NOT be given the benefit of the doubt in many cases, and given the lower grade. The school, which obviously as a grammar, already has very high expectations and standards, didn't seem to drop this approach at all when deciding CAGs, and seemed to award the lower grade where they were unsure about particular students. In the comp I am referring to, and in many others, I'm sure, they seemed to award the higher grade of the 2 possibles. making comparisons very very hard for that cohort when it comes to GCSEs.
I sometimes think there is bias against grammar school kids in cases like this. There is no leeway given to them at all by their own school. It's just expected that they will do well, and you're in trouble if you look as though you might drag the school's rep down. It doesn't matter what work and effort a pupil has put in to stay at the desired level in a grammar, or what their home life may be like, if all the unis see is "grammar school" on their application. I sometimes think that academic kids at some poor performing comps don't actually have to perform that well to stick out from the others. Without actual exams it makes it really hard to tell what the true ability actually is.