Interesting! But the first link you gave is just a list of conditions, which requires that I already know what my problem is. Is there a page that goes from symptoms to likely causes and what to do, like WebMD?
I'd say if I were to suggest improvements the symptom search could definitely be better and more prominently placed. In the UK I personally (and I'd imagine most people) get to the NHS website directly from Google, which is better at finding more relevant pages.
I’m not sure this is the prime “UX done well for symptoms->cause” example you cited it as. Though I agree UK government sites follow much better UX patterns!