I, uh, actually missed my grades (A*A*B instead of AAA - Oxford are
tough) but I'd love to help
I think HSPS is at Cambridge, isn't it? I preferred what seemed to be the more humanitarian approach at Ox.
I think your subjects are "better" than mine were, actually: I did English Literature and Classics as well, plus Art, and Physics to AS. And I have heard that Oxford look at percentage of A*s with GCSEs more than anything, in which case you're also at an advantage to where I was when I applied: I had 2 A*s and 8.5 As (the half being a short course in ICT).
However, my predicted grades were high, and I think my application really shone in the personal statement and reference...
I tried very hard to attach a meaning to everything I put into my PS: for instance, I not only wrote that I had been to Pompeii and various sites in Turkey, I drew a comparison between the humble holes in the ground I saw at a Turkish rescue dig and the large necropolis at Pompeii. I mentioned a couple of books, but more importantly I said what I had gained from them: "Victoria Finlay's book 'Color' began my interest in material culture as an anthropological source; Nigel Spivey’s ‘Greek Art’ made me appreciate its archaeological value in the case of ancient peoples we cannot experience first-hand and meant I could look at the Greek ruins I often see in Turkey from a more informed perspective." The course prospectus specifies an interest in
material culture, so I used that as a sort of buzzword.
The most useful advice I got for the PS - have a focus, some kind of interest you have which relates to arch and anth. It will pull the whole thing together and make it more cohesive. A friend focused his PS on the Ancient Persians when he applied the year before me, talking about how he first got interested in them, how he wrote an essay about them for a competition, etc. But it doesn't need to be that obvious; my focus was the way different societies can be completely different but spring from the same framework (if you think that's interesting you might want to research anthropological structuralism): I talked about the Pitt Rivers museum in Oxford (bit of sucking up maybe) since that's organised into purpose across different societies rather than place/time; talked about how people in Turkey deal with all the ancient stuff that keeps cropping up every time they're trying to build something as a mild nuisance vs. how a particular Aboriginal group in Australia (that I had met members of) sustain their ancient culture and merge it with modernisation/Westernisation.
I have three passports and have grown up in the Middle East; I played on my identity as a "third culture kid" to show how I am already used to moving through different societies as both an outsider and a participant, which is pretty much what an anthropologist does. If you have something like this, use it to your advantage!
Last thing: if you get to interview stage, they will give you objects and ask you to talk about them. Might be an idea to go to a museum and practise on the stuff there. Try to guess what it's made of, what it's for, etc.
Good luck! It really does look like an amazing course. I'm very happy with the place I got in the end (at SOAS) and think I will enjoy London more than Oxford, but am a little wistful that I won't get to study under one of the professors I met at interview who I absolutely loved.