I imagine in the UK, the police would come to a shooting too. In my experience, paramedics are sent ahead of the ambulance too - the paramedics can assess and start treatment before the ambulance arrives.
But this is fictional, and the the only way I can get my head round it is to think of it as a sort of alternative "fantasy" universe, where things happen differently. I believe that the "eight minutes" is actually a standard - ideally most life-threatening situations are supposed to get an ambulance response within eight minutes. It's not the "time and ambulance will take to arrive" - obviously that will vary and depend on different factors. I think the eight minutes has just been used as a plot point, and only "works" in the Sherlock universe.
