I hope to get to continuing
the discussion with Andy on the possibility of a utilitarian natural law theory (and, as I think, the necessity of it if utilitarians are to have an account of practical reason that even minimally makes use of fundamental principles like "Seek good"), but it might be a while before I get to it. In the meantime,
here (PDF; hat-tip:
Legal Theory Blog) is a discussion of rule consequentialism, which is the form of utilitarianism that I think most obviously shows similarities to natural law. The paper, by Richard Arneson, actually is a critique of rule consequentialism; but several of the objections are relevant to the issue as well.