Hey, I applied for the same course but the BSc!
I have contacted King's personally when I was doing my application, and I was assured that for courses such as Pharmacology, Biochemistry, Neuroscience (?), and Molecular Genetics they are willing to accept med. students due to the restrictions in the number of medical schools one is able to apply to.
Since you applied for the MSci it might be a bit tougher to get the place (higher requirements and maybe more people who are willing to study the course and also meet the requirements), but you should be fine for the most part. Try contacting them directly, or UCAS, and see what's available for you.