Haven't RTFT. But as both I and my husband, and our eldest child, are all Oxbridge, feel I can add some facts, hopefully without too much opinion!
DH went to one of the top four public schools as did his father and grandfather. He finished school, including an extra term of "Oxbridge" term as was then allowed, with three A-levels of B, C, and D. Got into Oxford with, as he does not fail to point out, the help of his main private school former-Oxford tutor calling his friends in the Oxford college. A college where his father and grandfather also went.
We met in the same college, studying the same subject, where I entered the same year, having lived just two years in an English-speaking country, child of two asylum-seekers. I was a full year younger than him and had 3 A's at A-level in a state school, where the one teacher in charge of university entrance had previously told me not to bother applying to Oxbridge.
BUT both my parents, before having to flee our home country, had been university professors and we were all very intellectual. DH's parents were and are positively anti-intellectual. They still think it's embarrassing the way I have books all over the house.
In case you're wondering, yes, I did feel very out of place back then, especially in my first year at Oxford. DH even now admits freely that it was absurd he was admitted at all, and says that he would never have got in without the personal pull of his public school tutor and his father's and grandfather's having been there. He tells everyone I'm brighter than him, which is frankly annoying, especially as he earns 5x more than me. Both of us grew very close to classmates whom we still see often and who DO sometimes tap us for contacts when changing jobs. None of that is a myth, I promise you, though it's not that anyone just walks into a job through connections; but at least they know where to apply and what to say.
Of our children, the eldest got into Cambridge, after refusing to try and carry on (compete with) the family tradition at Oxford. He attended one of the top four public schools, but not the one his father and so on went to. His offer from the Cambridge college required him to get 3 x A at A-level; he got four A. He was surprised to arrive and find himself with classmates who in some cases had got in with, say, 3 x B or even Cs. But as time passed, learned that they were not necessarily more stupid than he is. That alone, to me, justifies mixing the class groupings.
DS2 has SN and will not go to uni at all. DD didn't get into Oxford on A*AA, but has after all gone to a uni that is not only Russell Group but indeed generally agreed to be in the top 10 worldwide in English-speaking countries. Bear in mind that Oxbridge put a lot of emphasis on the interview, not just A-levels, and she is just not as confident in interviews as her older brother. And yes, I do think being female plays a real role here.
Summary? In a way, yes, it's harder to get in to Oxbridge now -- if you form part of that hereditary lucky class of men. I don't know if it's easier if you're not part of that insider group.
What I personally think is really unacceptable here in the UK is the vast gap in quality of education between Oxbridge and the rest of the universities -- including Russell Group. At Oxbridge teaching is almost entirely tutorial-based, so 1-to-1 or at most 1-to-3, face to face (apart from the pandemic), with lectures an add-on. You are more or less guaranteed to live in beautiful medieval or at least 18th century buildings all three years, with gardens. Many big companies will still automatically screen out all CVs from non-Oxbridge candidates, even if they got a First. To give you an idea, insiders still routinely ask, not which university you went to, but which college.
What most hits me about this, looking at the experience of my own children and friends' children, is how stark the difference is between Oxbridge and other universities. I think it comes down to funding as well as assumptions. Individual Oxbridge colleges have vast historical "foundations" ie money, even when the universities don't: and the colleges tend to put their funds where undergraduates benefit, while the university funds benefit graduate students. Other universities, even the best, get much of their funding from the government, and rely to a dismaying degree on taking foreign students paying higher fees. Students seem to learn mainly through large lecture halls with virtually no individual attention.
Even the best non-Oxbridge universities do not have the buildings and the space for full housing. The students have to find scattered places to live for one or more of their years, and sometimes part-time jobs, and don't have the time and money for clubs from sporting blues to the college newspaper to the Oxford Union. The Oxford Union, by the way, and the Oxford Conservative club, directly generated most of our current politicians and certainly ALL of the current Tory lot. Honestly, I look at DS1's experience and DD's experience and I grind my teeth -- and let's not even go into the help that my disabled DS2 gets. Then once you leave Oxbridge, everyone just assumes you must be good, even if you only got a 2:2.
Is a 2:2 student from Oxbridge really better than a 1st from St Andrews? I don't know. But ultimatelyI'd say the real problem is that it's time to do something about the huge quality gap, real and perceived. It's not enough to make sure a handful of the less privileged kids get in to Oxbridge, or that many more get in to university overall. Do something about the huge gap between any Oxbridge college and any other university! And what about all the people going into trades like carpentry and plumbing, which will never be replaced by Artificial Intelligence or outsourced to India?