Well, since nobody's given a serious answer yet, I might as well have a go:
There's no such thing as a 'best university' for medicine in the UK. Every medical school in the UK is overseen and accredited by the General Medical Council (GMC) so the syllabi are broadly similar at most medical schools, as are standards.
You may want to look at league tables if it means that much to you but, really, you will leave medical school with the same degree as everybody else and somebody who went to a university at the top of a particular league table will have little advantage over somebody who didn't when it comes to applying for foundation training.
The only 'best university' as far as medicine goes is down to you. You have to decide which university you like best, given the variation in
course structures, nightlife (very important for some people), financial considerations (e.g. if you're Scottish, you could graduate debt-free if you went to a Scottish university), distance from home (also important for some people) and, perhaps most importantly, what the admission criteria are. Each medical school has its own admission criteria so it's important to
apply with your strengths to maximise your chance of receiving an offer.
That last part is very important unless you're in the rare position of having a spotless academic record, high scores on admissions tests, a stellar personal statement and so on. As you're still doing ASs, I recommend you start doing some research on the application process from now so that you can plan ahead and make your application as good as possible in terms of getting relevant experience, being adequately prepared for admissions tests, all the while doing as well as possible on your ASs. Good luck.
Edit: I forgot to answer your last question! Assuming you take the standard route into medicine, don't take any gap years, and counting the current academic year, it would take you 7 - 8 years to become a junior doctor, depending on whether you undertake an intercalated degree (i.e. taking a year out during your medical degree to study something else) or not.