I did Classics on the UNIQ summer school last year!! It was the best decision I've made and the best week of that summer.
Since my subject's a bit different to yours and I'm not an expert at all at writing personal statements, I'll try to mention stuff I found most helpful last year.
For your statement the best advice I got was to try not to come out with sweeping, opinionated statements in an effort to sound really clever. Even though it's obvious I fell into that trap and I sounded like a right idiot until my teacher pointed it out. Be honest and concise!
You probably know that Oxford recommend mentioning wider reading on your statement, but don't forget to include a short opinion on the books/articles/speeches you put down. Although you do have a character limit, so don't feel you have to write an essay detailing why you think that - that's partially what the interview discussions will be about when you apply for real.
I went for short statements like 'I thought their criticism of this was unfair, it had some interesting points about that, etc' but if you have room for more explanation, go for it. And, of course, if you've done stuff related to your subject outside school (debating, etc) definitely put that down!
There's no harm in entering a few relevant essay or debating competitions to talk about in your statement, even if you don't get placed. It's a great way to say 'I enjoyed thinking about such-and-such a subject/topic/dilemma, etc in my entry' and sometimes Oxford colleges hold competitions like that for Year 12 students. I got to go to a Study Day at St John's for just entering a Classics essay competition, even though I didn't win one of the prizes! But I know there's not a lot of time to enter things like that between now and the UNIQ deadline. However, if you want something to embellish your actual application they can be really useful.
Don't leave your second choice blank! I was rejected from my first choice (English) and got into Classics for my second choice and LOVED it. Made me realise how much I loved the diversity of it and that it suited me more than a pure English course.
But if something happens and you don't get into Law but you do get into something like History or Humanities, it'll still help loads with your actual application as you still got into the school.
For example, I've heard about people who did Chemistry on UNIQ were accepted for Medicine and so on.
Get someone you know will be honest to read your statement - again, obvious, but essential.
If your school has a careers teacher, or maybe someone from the English department, it would be really helpful even just for grammar and spell check.
Even more obvious, stick to the website's guidelines like glue. They're telling you exactly what they want from you there. I used the advice there as a general paragraph structure for my statement to make sure I covered everything, if that's any help.
Apologies for including a lot of stuff Oxford have already written on their guidelines and advice for UNIQ and personal statements in general but they're the most important things I discovered when writing my statement. But just go for it is the best advice I can give.
And if you want to ask anything about UNIQ just drop me a message!
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