Littleham, my son is also reading History at Oxford. He absolutely loves it, if that's any help! Cambridge interview more people, yes, but I believe I'm right in saying that if you get an interview at Oxford you have a 40% chance of an offer (across all subjects, don't know if it's markedly different for History) whereas it's not such a good chance at Cambridge.
The other big difference in the interviews is that Oxford invite all interviewees to stay in their first choice college for at least one night (often three). This is helpful in giving them a better idea of what the place is like. Applicants who aren't going to get an offer from their first choice college may get an interview at a second college and this is all done during that residential period, so when you get your letter in early January with the outcome of the application, it's a final answer - 'Yes' from your first choice college, 'Yes' from another college or 'No'. (Very, very rarely apparently it's 'Yes, you've definitely got a place, but we'll tell you the college in August'.)
At Cambridge there are two rounds of interviews, so when their letters are sent out in early Jan, the answer may not be final - you could get 'Not sure yet, please come back for interview at another college on....' and then still end up with 'No' a few weeks later. I'd have found that tougher.
(There's a huge amount of information about admissions on both the Oxford and Cambridge websites which might be worth a look, if you have time.)
My son did get some support from his school with preparing for the HAT and the interview, but even if your daughter doesn't get much support that may not matter very much. As I understand it, the most important thing is to have done some wider reading and to be able to talk about it in an informed and critical way. Both the HAT and the interview, as I understand it, are designed to identify those who will get on best with the tutorial system, which is central to teaching at both universities. There are sample interviews on the web for both places, and those are definitely worth a look.
Good luck!