I think I actually prefer sharing in many ways. No, you don't get as much privacy as you might otherwise have but it can be awfully lonely when you are shut away in your room by yourself. As for your concern about not being offered accommodation.
I live in Arthur Tattersall (which is right by the Cruciform and main quad), out of the ten people living there, only two live a long way from London (Manchester and Monaco). The others live in South London, East London, Essex, Watford, and Amersham (I live in Hampshire). Hardly a long way away. Oh, and three of them are Medics, for what it's worth.
It's untrue that everybody gets accommodation, there are quite a few people that I know of who have not had accommodation from the start of term. But most people do (regardless of whether they live in London or not) and most of those who don't at the start get it in a few weeks' time.