You can get senior status at Oxford, which is much the same thing. UCL might allow it, too, I'm not sure.
Anyway, you'd need to contact them direct about the scholarships I suspect. If they're university-based, then they'll be able to set their own conditions. In my experience however Oxford at least tend to leave you to it, finance-wise, for second BAs and simply assume you've got the cash.
(PS - it's unfortunate you pick Medicine as your example, since that's the one degree for which you can get financial support!).