Some people still seem to think that Oxbridge is "not for the likes of us" or "only for rich kids", which certainly wasn't true when I was there 35 years ago, and is even less likely to be the case now.
Worryingly, some teachers seem to think this too, so schools do not do enough to foster Oxbridge entry. And when budgets and time are tight, the academic do not get the support they need. I've often seen the comment on MN, "oh well the bright will do well anywhere". Well they don't - or at least they don't achieve their full potential.
Elitism in sport, music and drama are encouraged in the education system, whereas academic elitism is not.
Some schools, pursuing league table positions, also do not encourage the bright kids to stick with traditional academic subjects, so a bright child who ends up with photography, drama and critical thinking as their A levels will be at a disadvantage in applying for any Russell Group uni.
DS1's (selective grammar) has an excellent program of support for entry to all universities - but Oxbridge in particular, from organised trips to open days, through assistance with personal statements, to practice interviews. They typically get 12-13% a year with Oxbridge offers. Given that the top 30% go to grammar in our area that's the top 3 or 4 % in the area.
That ought to be available for every LA - the top 4 % should be applying and should be supported in their applications.