You would need to study vet medicine at university. They have pretty high entry grades so you’d need A-levels in some sciences but you can look that up. If you could get some experience of what a vet does – work experience, that would look good and help you decide if you really want to do it.
In many ways being a vet is a lot harder than being a doctor. Doctors only have to know how the body works in once species (humans) while vets have to know how stuff works in lots of different species!
I would also recommend getting some experience by volunteering at a local vet. If it is something you really enjoy then you should get ready to work hard, as you need good grades to study a vet degree at university!