I agree with those who suggest that Oxbridge might be over-hyped. While Oxford and Cambridge might be the best for certain academic disciplines, there are other universities which stand out ahead of them in certain subjects.
For example, if a potential student wants to study environmental sciences, the the University of East Anglia is often rated as one of the best universities in the world for such subjects. Similarly, Southampton is rated as one of the best in the world for marine science, with UMIST excelling in engineering. For those subject areas (and many more) Oxford and Cambridge simply aren't the very best places to study.
However I'm still not sure that TTT's statement ("If you are good enough you'll get in, simples!") is actually true anyway. I hope that things might have improved since my teaching days but, somehow, I doubt it. In those days there was still a lot of unconscious bias in the selection process operated by Oxford (and by other 'prestigious' universities).
For example, I taught a 6th former who was expected to get top grades in all his subjects and was otherwise well-qualified for university entry. (i.e. he was articulate, conscientious, pleasant, sensible, responsible, involved in working with his local community and ticked every other box that those selecting candidates could possibly ask for). He applied to lots of universities, including Oxford, but didn't get a single offer.
Then he changed his name from (the obviously Asian) 'Fraz Taj' to (the very British sounding) 'David Christopher Parkinson' and re-submitted identical applications to the same universities. Every single one of them, including Oxford, then gave him good offers. (He actually accepted the Oxford offer and went on to study there).
I'm sure that every one of the admission tutors who saw his applications would have said (and, more worryingly, genuinely believed) that they weren't prejudiced against Asian students but they were clearly operating biased policies at a subconscious level nonetheless.