I realise I'm a few days late to this thread, but I figured I'd chip in anyway. I have wanted to do vet med since I was about 4 y/o (plans have changed a little recently, but that doesn't really matter at the moment), but I didn't manage to get the grades to get in. So instead, I ended up doing Animal Science at Nottingham, with the idea that I'd eventually go into either the accelerated graduate-entry vet med course, or just do it as another undergrad course.
Personally I agree with what people have said so far: if you have feedback as to why you were unsuccessful this time, and it's something that you can work on over the next year, then I'd definitely say try to do that
It's probably better to go straight into vet med as an undergrad, as it's difficult for most people to finance as a second degree (whether undergrad or postgrad). It's a little daunting when you realise that (if you were to take the Animal Science, or even Bioveterinary Science degree) you will have £27k+ debt before you even start the vet med course, then you either have to pay huge amounts in postgrad fees, or even just the £9k a year for another undergrad degree, with no tuition fee loans available. If you can handle that, or aren't bothered by it, then great, but I know it can be off-putting for some people (me included).
As some who is in their third year of Animal Science at Nottingham uni, I can probably answer questions you may have about the course/uni itself etc, so you're welcome to ask me for my 'insiders perspective'. Personally, doing this course has helped to open my eyes to a lot of other areas of interest and possible career opportunities, and I also have to say that I've enjoyed the degree a lot more than I thought I would, given I entered it as someone who just wanted to use it as a stepping stone on my way to a vet med degree.
As for your question as to whether to go for the Bioveterinary science offers, or the animal science offer, I'd say you should properly examine the course structure, modules you would be offered (if you have questions about the AS course at Nottingham, I can try and answer these), and maybe go to some campus open days for those courses and talk to the academics there if you wanted a more in depth perspective on what the course entails. I'd also say don't forget to think about the campus/teaching facilities themselves; for me, I massively preferred one campus to the others and that helped me make my final decision. Of course though, this last paragraph only really applies if you decide not to reapply for vet med.
So again, if you think you can improve your application for vet med in the next year or so, go for it. If you decide to do another degree, like AS or Biovet science, then just keep in mind the fees involved (both in taking the initial degree, and then doing vet med as a second degree). It's not impossible to fund, and I know a fair few people who are going down that route, but it depends how much finances impact your decision. But, I have to say, doing an Animal Science degree was not like a 'consolation prize' for me - it became a degree I thoroughly enjoyed in it's own right, and one that helped me discover other paths for my life that I hadn't previously considered