Funnyperson - the link you posted does not mention Oxbridge and the evidence for the claim you are making relates only to admission to Harvard and Yale. In fact the article explicitly states that:
'An admissions system based on non-academic factors often amounting to institutionalized venality would seem strange or even unthinkable among the top universities of most other advanced nations in Europe or Asia.' So the author is drawing a clear distinction between Ivy League admissions and admissions in other universities and other countries.
The claim he is making - that admissions practices were deliberately distorted originally to exclude high-achieving Jewish students - is a fascinating one which I had not encountered before. And he makes the allegation that the same practices are arising today in relation to Asian Americans. That requires a bit more unpicking. Because this relies on first accepting the premise that a very large number of places are being allocated to non-Asian American students (presumably white American students) purely on the basis of privilege and not academic merit and whilst he cites a wealth of data to support the claim that elite universities are not recruiting students whose ability profile matches that of the ability profile of America's ethnic minorities (i.e. whites are over-represented compared to how they do on a range of other indicators of ability) his evidence for systemic bias within admissions is mainly anecdotal and his causal explanation, that the universities don't want Asian students, is a little obscure (why not - he himself admits there is no financial case for discriminating against Asian students, the underlying causes must be multifactorial). Nevertheless it is a very interesting article.
But it is prima facie implausible to suggest that it simply transfers across to the UK.
There is a significant problem with ensuring parity of access for all minority ethnic groups but in this country students from non-White British backgrounds are over-represented in higher education and this trend has been going upwards for many years and looks set to continue to rise. See here.
The trend is not so pronounced but still evident when you look at Oxbridge. See here and here. You''ll note the representation of figures in these sources is obviously for PR purposes. There is a significant problem of measurement and comparison here when we try to define what is a student (f/t v p/t) and who belongs to an ethnic minority and if there is no data available whether we just assume the student is White British. And as I say we know that uptake of different courses is very patchy and maybe there are specific access issues which specific disciplines need to address.
Nevertheless the data available does not support a claim that universities generally or Oxbridge specifically are systematically trying to engineer Asian students out of places at their institutions.
I am involved in university admissions and seriously we just do not think about it that deeply. We are over-subscribed and we want to ensure that out of the 1500 applications we get for 200 places we get the smartest 200. That is all. That may mean that certain students are placed at a practical disadvantage in accessing the uni. I think that is a deep hard problem which a single university department probably doesn't hold the keys to and the article you linked to is right to highlight that university education has become a critical if not determinative route to securing privilege in our society. So if our admissions procedures routinely exclude specific social groups from access then universities will play an increasingly anti-progressive role in society. We should be self-critical and sensitive to the criticisms people make of us.
But the idea that we read applications from students from Black British backgrounds and think 'She's a high achiever, very suspicious, unless I can see a Gold DoE on the PS that's a no' - I think I can state categorically that probably isn't happening and it certainly isn't happening in my dept.