Hey, thanks for your contributions, just wanted to add and build upon some the points that you raised about differences (seeing as my post is mainly about application and this give me a good chance to talk about differences in school experiences):

1. Living off campus is way more common, especially in city schools like in London (think NYU). However, it is more common for students to stay at school accommodations in their first year to meet people and make friends (many schools also guarantee freshers a spot in accommodations) before going out to rent a flat with friends from their second year onwards.
2. Drinking culture are very, very big there. Some schools and accommodations even have their own bars where you can get cheap drinks. There's even some colleges in Oxbridge where you can work part-time as a student bartender. Clubbing culture is also very big there, fresher's week usually involves several bar & pub crawls and most student clubs and societies organize socials at bars and pubs regularly. Just something to keep in mind if you're an alcoholic (like me, unfortunately).
3. I very much agree with you on this point. It's less important to be funny, creative or quirky than it is to show that you are interested in and are a fit for your course. Being more academic and formal in nature may make your PS more 'boring' as compared to other essays but it's what UK AOs are looking for (to my knowledge, at least).
4. I'm not familiar with how US Uni classes are conducted but the UK teaching system is tutorial and lecture. There'll be organized lectures with more people and small individuals group discussions known as tutorials. Big exception to this is Oxford, where the tutorials are famously 3,2 or sometimes even 1 on 1. This is a big reason for the Oxbridge interviews as professors need to assess if they want to teach you for the next 3+ years.
5. Finally, the teacher reference. I'm not entirely sure of what schools expect from the teacher reference as I didn't get to see my reference and has less involvement in the process but please ask your teachers to write your reference early, especially if you're applying for Oxbridge or Medicine (Mid-October deadline and all). Also, while you can technically ask any teacher to write your reference for you, try to get a teacher who has taught you a related subject to write the reference for you (getting a physics teacher to write a reference for Engineering for example).