Probably around the same time DC were at Westminster School.
The top maths set there was small and phenomenal. Eight students, one of whom had original research published whilst still in sixth form. (She had been invited to a prestigious summer camp in the US and this was the product.) Despite this she apparently was not the brightest in the group.
None of the four DD was friendly with went to Oxbridge. Two went to the US (Harvard and possibly MIT) whilst two went to Imperial. In other subjects as well Oxbridge regularly missed some very strong applicants, though in fairness some of the surprises were the other way. I remember in particular one astonishing boy who was good at everything. Really good at everything: sport, music and academics, who only got in through the pool, but who then stayed on to take a PhD. Over time Westminster's Oxbridge acceptance rates have declined, and more are going to the US, London and increasingly,. elsewhere in the world. The calibre of applicants is unlikely to have changed much, nor will the teaching have changed.
The questions is then whether Oxbridge by spreading the net wider and looking for unpolished diamonds is picking up students with greater potential. If it is, well done to them. If not, and they are passing over good applicants for political reasons, their falling position in the league tables might have an explanation.
A decade ago when parents swapped news of where their DC were going, English parents would almost commiserate when I mentioned LSE. Overseas parents, often with finance jobs, took a different approach. As far as they were concerned LSE was "a great school" and a place there was something to be pound of.
MN too. A decade ago there was a weird poster who kept rubbishing Imperial. It was one reason I started posting as it seemed crazy to advise strong students to rule out one of the very best STEM universities in the world without proper consideration. (It turned out the poster had had a DD who had studied fashion in London and had not enjoyed it, which had led to a general animus against studying in London.) Things have changed and people probably accept "Loxbridge".
In terms of mobility London University have quite a good track record in partnering London schools and the built in advantage that going away to University is not the norm for many London families. You then get an odd mix. Plenty from private schools who can afford to live in London and plenty, often East European or other ethnic minorities from London, many of whom will have been through good grammars or magnet sixth forms. (Or benefitted from private school bursaries.) In contrast there is probably an underrepresentation of middle or working class kids from the north. Given the large number of overseas students, and the strong focus on subject, differences in background seem to be less obvious.