OP I think I probably was at uni with them (or their sisters). I'd hoped they'd have grown out of it by now. 😉
I've met a few women like this since (also some of their French counterparts - it's not just a British thing).
My advice would first be to not worry if they don't like you. In fact it's positive, because they tend to only like women like them.
Secondly you have two options. Either try to be like them (not advised), or focus on inhabiting who you are totally unashamedly. So, she makes the bitchy comment about you birthday present (and here's no doubt that that wasn't a neutral observation!) and you reply with something along the lines of "wow weren't you lucky, that wasn't normal for my friends when we were 16". And say it nicely but rooted in yourself, not trying to win her over (you won't). The point is to assert yourself and not let your history be made "less than".
Their behaviour can make you feel really bad or inferior. The reasons behind it maybe aren't relevant (but I agree with what you've said so I think you know anyway). The people I've seen who manage to rub along with women like this are the ones who are solid in their own background and identity, and unashamedly so. So basically it's obvious you're not trying to be like them, you see there's a difference but hold yourself and your life experiences equally valid.
And making a joke about their bitchy comments can help too. So to things like the "[pause] boarding school" remark, it's ok to laugh and say "aah yes! Boarding school! Such a funny British thing!" as though she was talking about cycling to school on a unicycle. A sort of curiosity!
And for this, your non-British status, as well as specifically Australianness is a great advantage!
But please try to make sure you guys socialise with other people too. You can't spend the rest of your life doing dinners/weekends away with only them. Because they may change their attitude towards you later (maybe not) but in the meantime, you need to be around women who are actively nice.