You have to laugh or you'd cry.
last year I saw my doctor 2 weeks before my sicknote was due to run out he did a new one which I sent off. DWP returned it and said you cannot send in a predated one as you might be better by then. Despite explaining that there is no cure and no chance of one they wouldn't accept it and I had to get an appointment for the day before and have him date it from the following day.
I rang up yesterday to make appt. The earliest I could get with my Dr was May 15th. I booked it. I might be better (or worse) by then but I figure I also might have something else wrong with me in a month's time. In the mean time I booked to see the nurse, that's on May 1st.... Still there's always the A&E 40 miles away in next town. We've only got a minor injuries unit here.
I live on the south coast and can book appointments on line with my surgery. As long as you don't mind which doctor you see you can sometimes get an appointment the same day but nearly always the following day. They are happy to ring you at home to carry out a consultation if appropriate and all repeat prescriptions can be ordered on line.