As I understand the rules, those that apply for a course that is at the same level as a qualification that is already held are excluded from access to further student loans i.e a graduate cannot access a student loan to study another undergraduate degree. That said I believe this rule does not cover graduates who wish to study medicine, therefore they can access students loans.
The £20k mentioned below is for the current MD qualification. If you want to estimate the fees that a BU graduate medical degree may cost look at what international students currently pay at other medical schools, £12k pa for the first two years rising to £20k pa for the three medical training years.
All universities are private institutions (they are not owned by the government) but all but Buckingham rely on government funding to subsidise undergraduate teaching, that is why the cost of a medical degree from Buckingham is likely to mirror fees for international students.....if that makes sense??