I applied to Nottingham, for Biology.
I think Medicine is competitive but it depends on how many of the eligibility criteria apply to you, so you may be more likely or less likely to get in depending on your circumstances.
The thing about being on your own is that most of the other people will be there on their own too, but everyone should be kind of similar as you all want to do the same thing and have similar backgrounds, i.e. parents didn't go to university.
Why would you have to fly? There are courses in universities that are spread out over the UK...