Hii, also international (from Canada) applying to veterinary in the UK!! Sounds like you are on the right track, it may be good to try and get some large animal experience if you only have small animal, but I get how its pretty difficult to find opportunities. You could maybe look into any farms, or riding schools as those usually give good experience with cows, horses, etc.
For my personal statement, I wrote about what moment made me realize I wanted to be a vet despite all the challenges I have faced working in a clinic. I also wrote about the skills I have gained/learned from my experiences/volunteering and how it shapes me as a person and a future vet. Hope that can help give you some ideas!
Other than that, I think it may be good to consider how you will be financing vet school, as international fees are kinda crazy and some schools have higher tuition than others and some with higher cost of living.
Good luck with your applications!!