Law undergrad at Cambridge here (and received offers from LSE, Warwick, Manchester and QMUL).
Always remember this: for an academic PS you want to RELATE EVERYTHING TO LEGAL STUDY.
1. Reading
An academic PS deals primarily with theoretical points of controversy within the subject. This means you need to know exactly what you'll be studying at uni, which means you need to have read materials that correspond to legal study. Mentioning your reading is important because 90% of the time it's what you'll be doing at uni.
The important thing is reflecting on the reading and showing insight – what was your instinctive reaction? Did it make sense? Why/why not? What does this tell you about the law? Why does it make you want to study it? Fleshing out a few points in good detail is what you want to do. Don't just name-drop books for the sake of it (I only put 3 books in my PS).
2. Subject related extra-curriculars
Court visits, mooting, debating, law firm/chambers work experience, shadowing scheme, summer school etc – it's not academic unless you relate it directly to legal study.
E.g. this is how you turn a court visit into an academic point: "I witnessed an intriguing case at the Crown Court where the defendant faced a rape conviction under the Sexual Offences Act 2003. During his cross-examination I doubted whether the term 'rapist' properly applied to the facts of the case. I followed up my uncertainty with Ashworth and Horder's explanation of fair labelling in 'Principles of Criminal Law', whereupon I solidified my opinion that the moral censure associated with the label was at a mismatch with the case I oversaw."
An extra-curricular is made academic when you relate it to legal study.
3. Extra-curriculars unrelated to subject
School leadership, sports, music, etc. If you want an academic PS, you keep discussion of this to a minimum. I wrote around 100 words about this, condensing only the most noteworthy things into one small paragraph (about 6% of my PS).
4. Organisation
An academic way of organising your PS is splitting it into identifiable topics, e.g. first paragraph mainly on the rule of law (public law). the second paragraph mainly on strict liability (criminal law) etc. One paragraph can have two topics, but keep it clear and don't muddle between topics unnecessarily.
That's about it in a nutshell.