If you vaccinate an animal against TB you won't be able to distinguish the reaction caused by the vaccine or by real infection. Also it is not very effective protection-wise (not as good as some respiratory disease vaccines or other products for sheep) and it could effectively mask carrier animals which you wouldn't cull thinking they were vaccinated, where in fact they are spreading it. Also blood testing doesn't work in this case, as the immune response to the TB bacteria is very different to, say, a viral respiratory infection. There is a collateral test for TB, other than the usual skin test, but it is not considered good enough to replace the skin test. Unfortunately for this disease, it is not the case of choosing the best test between many, but choose the least bad between just two!!
One of the reasons why they vaccinate badgers is because they are supposed to be "protected" species and in theory (unless authorized centrally, as is the case for the current culls) cannot be killed. Same does not apply to farmed species and I agree is very unfair. However, it is generally agreed that people are more likely to pick up TB from their farm animals/pets than from a badger - at least I would. I'd have more contact with my cows (coughing in my air all the time) than with a badger somewhere in the woods. I think that is why there's less tolerance for TB on farms.
Also animals are not to be treated/vaccinated because there are very few drugs that can kill the bacteria, and there is widespread concern that by treating all species the bugs will get resistant to the few drugs and in that case we'd start seeing people dying of TB again. Surely we don't want that?