Hmm don't like how you declare it isn't an issue suddenly. Just being interested in "anything medical" is not a reason to apply for medicine. If that's your only reason then apply for biomedical science or pharmacology or one of the many other medically-orientated degrees. The reason you apply to
medicine is because you want to dedicate your life to being a
doctor. You haven't mentioned anything about the career which makes me think you have not done even basic research yet. Which is fine - its early days - but it is something you need to do before you proceed further. Your work experience when you arrange it will tell you more about what the career is like.
Why? What experience of being a student at Oxbridge do you have? My guess its 'what i see on TV' which is totally wrong and inadequate. Did you know, for instance, that the majority of students are from state schools? Did you know that the percentage of private school students at UCL, your supposed not-posh alternative, is only a
handful of percentage points behind Oxbridge and one of the very highest in the country (plus it'll be even higher for medicine)? If you're actually worried about going to school with private schooled people then you're going to need to go way, way down the league tables to avoid them, and certainly drop the thought of studying medicine!
The reality is that Oxford and Cambridge are fairly middle-class places, but so are all of the top unis, and in reality the few very rich people you'll meet (there will be some) are still nice, normal people who are a bit scared and looking to make friends like everyone else.
You should attend one of the events mentioned above by jneill (PRSOM) or at the very least the open days.
I went to a state comp and had a fantastic time at Oxford. Definitely recommended as an amazing place to study.
For like History etc yes, but if you are going for medicine the differences will be reduced. There are more important factors in applying to med school than that (course structure, teaching style etc. Once you've spent some time and found out whether you want to do medicine or not you can come back on TSR and find out more!