In my experience so far as a first year at Liverpool, it is very easy to meet people outside of the course through sports, societies, and if you live in halls you are unlikely to be put with other vets except maybe 1, I have a flat of 8 and no other vets but have a medic and others who do business, computer science and essay subjects. I always used to think I wouldn't want to have too many vet friends because I thought that might stress me out discussing work etc and maybe a competitive aspect, but actually I've done a 180 being here and pretty much am only friends with other vet students, mostly who are more 'chilled' rather than focused on work 24/7 so we equally stress and vent to each other which can be helpful. But I know a lot of other vets who do prefer people from other subjects, and some also do music/acting/arts societies etc, there are a lot of students from all sorts of walks of life with different interests, not everyone is strictly only focused on the degree and nothing else.
There are different types of unis with some being city unis vs campus unis, where if you have a whole vet campus or with related subjects (e.g. RVC is mostly all vet-related, Nottingham has the Sutton Bonington campus with mostly vets and only few other subjects) then it may be harder to meet other people from different subjects, but still not impossible in the same way with societies etc, and for example in Liverpool you move to a separate vet campus in 4th year too. So I would just research into the types of unis that may suit you best and apply to those - but uni even if it is a mostly vet-based campus you can still find ways to meet other people and all of them will have various societies to engage with separate hobbies.