You won't be able to transfer courses. It would be very, very rare (if ever) that this happened, but even then it would only be with related courses like maybe med to vet med, but I doubt even that happens tbh.
I would say you need to decide firstly if you def want to do vet med - book a week at a vets and see what you think of that, and then reevaluate.
If you do decide to go for it, tbh you are much better trying to apply as a first time undergrad, even if it means a gap year or two. You would need the right grades and subjects, plus work experience at vets/farms etc. You can apply as a graduate applicant (ie: using your degree as the qualification for entry) but with something like maths you wouldn't have covered the science background, so would be applying for the normal course (so would probably need the right alevel/highs quals as well). It is then silly money to do this at most unis (circa £18-22K per year). Except RVC and Nottm which are cheaper, but then very, very competitive for grads because of this.
I would really, really, strongly suggest not going down the grad route if you can avoid it. But, before you decide anything, do some work experience and see what you actually think of the job in reality!