Obviously this isn't great evidence but when doctors at work have asked me where I'm applying/going and I say "Southampton" a very common answer is "oh that's a good place to go" and when I say UEA they don't say anything. I actually think this is kind of ridiculous as there's no evidence to suggest Southampton is any better at producing doctors than any other university.
There's evidence of this sort of thing from all over the place and certainly isn't limited to medicine. If you're in a medical career at Mid-Staffs, despite it's quality now being very good, people will still notice it. They may even consciously think about how it shouldn't make a difference but these things can swing opinions.
Peoples' (job interviewer) perceptions (whether based on truth or not) can change the outcome of decisions and I suppose it means it could affect your prospects after you leave university. It shouldn't though.
I'm not sure if this is coincidence either but I've noticed the vast majority of surgeons I've met (traditionally one of the harder posts to get into) come from 'mum and dad list' universities like Oxbridge and the London universities. This may be more due to the fact I work in a London hospital however...