So how did Jenny get into Oxford again??

The teacher wasn't ashamed of going to Cambridge. She looked down to the floor because she knew she was about to lose the argument with Jenny (the "going to college makes you successful in life, and leeds to new and exciting things" one) once she confesses she went to a really good college but didn't come to much success, or adventure.
Did you go to Cambridge? Is that why you were offended by her misunderstood reaction?

Much that once was is lost, for none now live who remember it.

I thought the teachers sad look was because she went to Cambridge and ended up just teaching "semi illiterate" schoolgirls who "wrote essays about ponies". She wasted an exemplary education.

You are massively wrong coolaree. Cambridge and Oxford have always , at least for convenience sake, been regarded as academic equals overall. It's why the portmanteau Oxbridge exists. In fact, for many of the past 15 years, Cambridge has been ranked as slightly better in just about every subject. Plus Cambridge always has a better reputation in Mathematics. In fact , Warwick frequently gets ranked above Oxford for mathematics. But for Politics Oxford usually comes out top and St Andrews and Sheffield often rank above Cambridge for that subject. Not that you could tell from watching their union debates online (Cambridge's union actually older) where the debates are far more political , sociological and mature than Oxford's entertainer obsessed agenda. None of this says anything about individual students who'll more or less conform to what's expected (I wonder how many pay for someone online to write their essay). Oh, maybe 1 in 50 are amongst the wittiest people you've ever met but that's started at school, not university and what about the other 49? Universities are businesses these days.

As for getting in Oxford, it's a common misconception that it's harder to get in to Oxford or Cambridge than any other UK university. In fact, enough people are put off from ever applying, either by their own assessment of their preferences or the advice of their own college, that approximately 1 in 4 of all applications to Oxford and Cambridge result in being accepted (or at least being made an offer). So the filtering out is mostly done before the actual applications and interview stage anyway.

Compare that to some other top universities where the acceptance rate is more like 1 in 10-15 for the same subject, possibly because there's a wider range of talents all thinking they might be good enough for that level but not necessarily thinking, rightly or wrongly, they'd be good enough for Oxford or Cambridge level. It is said to sometimes be easier to be accepted for Oxford or Cambridge than it is for Edinburgh. Plus universities used to know whether you were also applying for Oxford or Cambridge so some other top universities would enviously/cannily not make you an offer so as to have a greater likelihood of 'likely to end up coming here' offers. So Oxford is not necessarily the hardest university to get an offer for if your grades are relatively reliably strong and if your personality is deemed that you'd get the most from Oxford and it from you.
The university was founded a long time ago and, since then, many other universities have come along and some will, inevitably, arguably do some things better and bigger.

And then, believe it or not, being satisfied that you were good enough for that year's intake to be deemed 'Oxbridge material', quite often you only had to get the bare minimum in your actual A-Levels (yes, as low as 2 E grades). The idea was to take some pressure off you or something, or that if Oxford or Cambridge said you were good enough then you were regardless of whether you decided to relax a bit before actually commencing the harder work at university.

In the 1960s, which school you'd been to mattered far more as to your chances of being accepted. Lynn Barber, on who the character is based, went to a private school, Lady Eleanor Holles School , established in 1711.