What are Oxford and Cambridge looking for in a personal statement?

The Oxbridge personal statement style is slightly different from that of other universities, and it is important that you don’t cater your statement towards one university in particular. While it is true that there is lots of overlap and common ground in what your personal statement should be ‘saying’ (and even then, your statement cannot be right or wrong), Oxbridge are definitely looking for particular things.
The most important of these is, undoubtedly, enthusiasm. The entirety of the Oxbridge admission systems seeks to find students who are passionate about their subjects, and you need to convey this as best you can in 4000 characters. Explain exactly why you love your subject - be honest and sincere, and use examples as evidence of this (next point!). Secondly, it is imperative that you talk about relevant literature or media you have independently sourced in order to both show this interest in your subject, as well as your ability to go beyond the A-level curriculum. Although this is important when applying to any top university, it is absolutely crucial that you do not talk about books that you haven’t read - you do not want to find yourself sat in an interview having to blag your way through Dickens’ novels if you’ve never even heard of David Copperfield. Thirdly, you will have to make sacrifices on the extra-curricular front. To put it bluntly, Oxbridge don’t particularly care about your non-academic pursuits, but that is not to say you shouldn’t put any in. They can convey well-roundedness and personality, something less important in Oxbridge admissions pre-interview but more important to other universities.
Remember that your personal statement is not only going to Oxford or Cambridge - you’re applying to five different universities, so make sure that whilst you’re meeting what Oxbridge is looking for, you’re creating a versatile and well-rounded statement that reflects exactly why you want to study your subject. Good luck!