> Also, if problems aren't certain as they are chronic, widespread or hard to diagnose you see certain specialists who are trained to diagnose. You don't see a general physician

This is actually (imo) one of the largest failings in the UK's various health systems -- Diagnosticians as you have them in the US, do not exist. The entire system relies on GPs keeping up to date on various diseases and symptoms. This means that a lot of the time diseases that typically present with vague symptoms, like cancer, can go undiagnosed for years.