DC were at a very selective private school which gets one of the highest numbers of Oxbridge acceptance rates in the country.
They also get a number of near misses. Students with A*s who don't get places, but who go on to do very well elsewhere.
Admissions are not an exact science. A course might change its selection criteria and pupils who might be expected to get in, did not. And then a few years down the line, there would again be pupils being offered places.
The school's advice was not to get hung up on Oxbridge. So DS was advised to apply for the top four, and heavily oversubscribed, courses and accept whatever he was offered. As Stranger suggests, those courses that interview will be pick up a slightly different mix than those that do not, so there are plenty of A*s in lecture rooms elsewhere. The top four courses in most subjects will keep the same doors open, and by and large, though dreaming spires have their appeal, other places off other advantages.
The second piece of advice was to treat University application as a two year process. Medics often do this, but the same principles apply to other oversubscribed subjects. If you are a strong applicant, and you get your grades, it is worth doing your best to get a place on a demanding course. It does seem easier with achieved grades, plus you have experience and maturity on your side. Often scientists and mathematicians, if they were not keen on Imperial, would try Cambridge first and Oxford second, the latter seen as a tad less competitive. A couple, PPEists, only applied to Oxford first time round knowing they would reapply if unsuccessful, and not wanting to irritate alternatives.
And increasing numbers, including some of the very brightest, apply to the US, either in parallel or as an alternative. Top British Universities compete at a world level, and to a large extent need to recruit the best students they can, regardless of background. International students, particularly at Masters level (GradCafe) spend a lot of time discussing the relative merits of LSE, Stockholm or Singapore. And those perceived reputations feed into both staff and UG recruitment, and presumably access to research funding and alumni support.
For those near London there is an American play called Admissions on at the Trafalgar Studios which looks at issues around liberal angst and positive discrimination in the college process. Recommended!