Get a degree in something else first, then apply to another undergraduate degree.
I know a law lecturer who desperately wanted to do law, but presumably couldn't get into a good law school, so she did something irrelevant first (at Harvard), then she did again something irrelevant for her master's (at LSE), and finally the LLB she wanted at Cambridge.
A friend of mine who's doing medicine (MBBS which are two undergraduate degrees here in Hong Kong) but did his BA first at Oxford in psychology.
Now I don't think you need to do your bachelor in any of those schools to get into medical school, as being a graduate should already give you a significant advantage over other applicants. But of course you will need time and money.