I’m a registered vet nurse (diploma, not degree). I also didn’t do my a levels, I did a national extended diploma in animal management (triple distinction* result). Having applied to vet med (oct 2022), personally, I don’t think you would be able to apply for both without prioritising one. Vet med is such a competitive course to get on to that your personal statement will completely reflect your desire for this career choice and will leave questions as to why you’re applying for vet nursing - vet nursing is too competitive in its own manner (RVC for definite doesn’t come up on clearing, not too sure about Harper Adams etc), therefore, applicants personal statements too will demonstrate their desire for this career choice. For definite, you can use the vet nursing degree to get on to vet med, but if you are weighing up whether you want to be a nurse or vet, personally, you need to consider this before applying. See practice and see what us nurses do and what the vets do. Look at the role, the time/commitment to study, responsibility, work/life balance, the entry requirement - obviously vet medicine will require much higher grades. If you don’t have that ATM but do want to be a vet, that’s OK, but you will need to achieve the grades.
They’re very different jobs, so you will need to consider what role in practice would suit you best. As I said, if you wish to change career after becoming a nurse, you can do it. I know plenty of nurses who are at vet school or who are qualified vets now. But personally, I don’t think applying for both courses at the same time is the best choice. If you are considering vet med and want a 5th choice, you’re best picking bioveterinary science or biology etc. Hope this helps