I turned down Cambridge for a RG (for the course). Slightly regret it now. 20 years later, career in technology, barely give it a second thought and hardly ever get asked about where I went to university. However, last job I went for, the HR guy mentioned that my masters at LSE made him want to interview me because "you must be clever to have gone there". He was in his late sixties though. I find younger people dont really care, though they are still looking for "a good degree" i.e from a fairly prestigious university. I really dont think it has to be Oxbridge anynore, although certain professions are looking for that plus a few others eg being a City analyst probably still requires a Math degree from Oxbridge, Warick and maybe a few others. But thats one thing to do with your life out of millions!
I do find the secondary schools are a bit obsessed with it, mainly because its part of the marketing blurb now isnt it, GCSE stats, A levels stats and Oxbridge admissions number. I find that annoying and pointless as its only ever going to apply to the top 5% of nerdy types (I was one before you attack!) who are happy to spend their teenage years studying, and would probably get there, if they wanted to, from most schools. Also there's the medics and lawyers cohort in a similar bracket who dont seem bothered about Oxbridge?
I also know a few parents who have been telling me since Reception that their, admitedly bright, children are destined for Oxbridge (never one or the other, like they're exactly the same) which I find slightly contemptible as its all about them and the showing off potential, not the child.Usually from parents who didnt go to university themeselves, who also tell me its essential to have an Oxbridge degree to work in the City or in Finance, which is absolute bollocks of course. I have far more admiration for the children whose mother's tell me post-GCSE that they're thinking about it and then get in. Good for them I say. But its not essential for a successful and happy life.
My children aren't in that bracket so we will have the whole range of further education choices to look at. As someone who has been academically successful and professionally pretty successful, but who suffers from anxiety and stress, I am actually quite pleased about that.