MPH courses are probably one of the more difficult Masters courses to get into. I would say a lot of people coming onto those courses have previous experience in healthcare, and quite a few courses specify the need for experienced people. Sort of like an MBA. I don't think your chances would be very good at all without experience and a with 3rd class honours.
You could possibly do an Open University degree, or apply for distance courses where spaces are not so limited, though. Possibly even an MPH through the University of London external program, but I'm not sure how much they ration places.