“it could indeed mean that we spend the entire NHS bill on one patient, and then two months later have no money for the next patients. In my view this is entirely consistent and moral”
Something is deeply wrong with your theory of morality.

Personally I believe that we should talk less about rights and more about moral obligations, as a “right” basically means a statement of “ought to have something done to you by someone else”, which in reality is an obligation relating to other people, not the the object of the action. So, I would suggest that people (not “society”, which is a useless abstraction), have a moral obligation to save someone else’s life whenever possible, regardless of the cost. Since this can only be applicable on a case-by-case basis, it could indeed mean that we spend the entire NHS bill on one patient, and then two months later have no money for the next patients. In my view this is entirely consistent and moral, since there is absolutely no way that humans can make the decision of how much we ought to help each person, and how best to divide our resources for health.

On the issue of education, I wouldn’t really suggest that anyone has a “right” to an education, since medieval peasants simply worked the land for a living and there is nothing immoral about that situation - they weren’t having their “rights” violated. However, I would suggest that spending money on education, whether it’s basic arithmetic or medieval art history, is intrinsically desirible, if not necessary. That is to say, there are many things that we are not obliged to pay for, but that it’s quite nice to.

Anyway, I call for less libertarian ranting about how poor people have no rights on this blog (not that it isn’t well thought-out and argued in places), and for some more genuinely conservative contributions!