"Why can't I make an appointment?"

I have a blood test on Friday. The surgery calls me on Tuesday to tell me that I need to make an appointment to see a Dr. I ask if we can make that appointment during the call and they say no, call back after Monday. This will another lengthy wait on the phone.

Why identify a problem if I then can't get it treated? Why can't I book an appointment more than a week in advance? This approach is woefully inefficient. The medical care may be passable on the odd occasion that you may actually get to speak with a clinician but the administration of the practice is truly awful.