NHS already offers a (fairly rudimentary, last I checked) diagnostic tool in the form of NHS 111, which as well as being a phone number that people in the UK can call to talk to someone, is also a website (https://111.nhs.uk/) where you can give your symptom(s) and get a suggestion if possible causes.
It may not yet be good enough in all cases, I'm not sure, but is that what you're asking for? I'm not quite sure as you dived into things like data licensing without being clear on your actual hoped end result.
(Of course, the 111 site is designed as part of the wider NHS system, so when in doubt it's more likely to give advice to speak to a GP / call to speak to a nurse / visit a hospital, than to say "not sure, here are all the conditions it could be". But as it gets better I expect it to be able to do both.)
Not to mention that the main NHS site also lets you search for symptoms in the main search bar, so you don't need to know the condition to use it to search for possible conditions. edit: as better pointed out by jjar here https://news.ycombinator.com/item?id=32650958
It may not yet be good enough in all cases, I'm not sure, but is that what you're asking for? I'm not quite sure as you dived into things like data licensing without being clear on your actual hoped end result.
(Of course, the 111 site is designed as part of the wider NHS system, so when in doubt it's more likely to give advice to speak to a GP / call to speak to a nurse / visit a hospital, than to say "not sure, here are all the conditions it could be". But as it gets better I expect it to be able to do both.)
Not to mention that the main NHS site also lets you search for symptoms in the main search bar, so you don't need to know the condition to use it to search for possible conditions. edit: as better pointed out by jjar here https://news.ycombinator.com/item?id=32650958