Hiya. I'm glad you're encouraging your niece to 'aim high'.
Personally, I would encourage her to look carefully at the courses on offer, as well as considering the social/financial side of things. I know that in my own subject area the syllabus in Oxford (less so in Cambridge, interestingly) is very old-fashioned and the whole system is very resistant to change. I can't tell you much about history, I'm afraid, but personally I'd only encourage A'level students in my subject to go to Oxford (and there are LOTS of good things about Oxford, so please don't think I'm running it down) if they were prepared for the kind of syllabus they'd find there.
I also know from talking to colleagues who did go to Oxford that the system can feel very pressured and may not suit all students. (Better if you're the confident type, for example.)
I'm sorry about your own experience of being uninspired by lecturers and courses at your university. I had the opposite experience. Went to a provincial redbrick university (of the type I now teach in, though actually less prestigious than where I am now) and found excellent teaching (with one or two rare exceptions) which turned me on to my subject to such an extent that I stayed to do a PhD and am now a lecturer in the subject myself. Provincial universities are often staffed by highly committed and intelligent people, who are just desperate to share their knowledge with intelligent and committed young people like your niece. Don't discount the redbricks just because of your own experience.
Having said that, I was in Cambridge last week, and their students are very good and the one-to-one tuition that students get in Oxford and Cambridge clearly pays off in lots of ways (they write very well and are able to express their ideas fluently and clearly, for example). I have also taught in Oxford and again found the students interested and interesting. I am not convinced that Oxbridge is necessarily 'better' than elsewhere, but let's just say that the 'lowest common denominator' there is higher than elsewhere (... does that make sense? I mean that fewer students are really struggling, though the best will do well anywhere).
I am not trying to put your niece off trying for Oxford or Cambridge, but I am just encouraging her to see that there are also other good places where she might go... Could she arrange to go to Oxford for an Open Day to have a look around and talk to some people? That might reassure her that it's not some scary place people solely by toffs! Both Oxford and Cambridge have made huge efforts in recent years to attract students from state schools and I'm sure their respective history departments would be pleased to hear from her.
Hope this helps and doesn't sound too negative (it wasn't meant to be).
PS I didn't get in to Oxford at 18 (so I may have a chip on my shoulder) but it definitely hasn't held me back academically!