Medical calendars

I wish there was a common online calendar service that various NHS trusts used. Then a) I could set my email/SMS reminders globally; b) it could export live calendars so I could integrate it into Google Calendar or my phone and have new appointments just appear; c) it could check for clashes where two different medical services want me at the same time. I know how it would work at a technical level, but how it would be managed and paid for is beyond my comprehension, so I suppose I can't make it happen.