Tollund, I'll be in honest in saying that the very thing I get most frustrated about vegetarians is selective or competitive ethics and I do think you are a little guilty of this with what you have posted in this thread.
I think you do need to be more aware just how many drugs are tested on animals and be realistic about it than perhaps you are from your posts. However I do agree that I think its important that you should know whats in the medication if it worries you.
You need to be able make an informed decision and so you can take medication you feel as happy as possible with if this is such a strong concern of yours. You may ultimately may have a stark choice of refusing medication or compromising your ethics, but you should be in a position to make that the decision about where you think the line in the sand for you is, and be as comfortable as possible when you do that. Its not up to anyone else to draw that line. Only you can do that.
I don't think thats trivial or petty like others are suggesting. And in this case I don't think your request was an 'out-there' request which isn't easily accommodated. Being vegetarian or vegan is pretty common and these type of question are ones that you won't have been the first, nor the last, to raise. We are all different and certain things are a lot more important to some people and not to others especially when it comes to our health. The NHS is great, but it shouldn't be a conveyer belt or machine that treats patients are something to be processed not listened to, even when there are the financial concerns, there are at the moment. Good health is about emotional wellbeing being part of the package of physical health and shouldn't be overlooked.
I think this is about addressing patient concerns effectively and properly. Afterall, if its going to haunt you and plague you with guilt or you feel forced to have a drug its not a productive outcome.
Its also particularly of note, you are talking about anti-biotics which have particularly characteristics as drugs. If you are given them, you need to be taken for the full length of the course otherwise it has the potential to stop the drugs being as effective in future - which is a potential harmful problem. If you are uncomfortable for whatever reason taking the drugs, you are far more likely not to complete the course; that has implications for your health and potentially for other people's health.
People might not agree with your moral stance on the limits of your vegetarianism. As I've said, I don't particularly. I don't think you have necessarily have a right to other drugs on the NHS, but I do think you have a right to be fully informed and properly reassured to the best ability of the HCP treating you so that you can make decisions about your health that you are happy with.