GP requested appointment but none available

Summary: GP requested appointment but none available

,I received a phone call on a Thursday. My regular GP had asked for me to come in for a face to face appointment following results of some tests. The time I was offered clashed with another commitment. There was no other appointment available on that day.
I asked if I could come in on the Friday, but I was told I could not make an appointment for the following day because the surgery only offer “on the day” appointments or 7 or 14 day prebookable. I was given a 7 day prebookable for the following Thursday. This meant I had a full week in which to worry about my test results.
I rang the following day hoping to get an on the day appointment. There were no appointments available. I made the phone call at 8am and was in a queue in excess of 30.
This appointment system is all wrong. Patients who are ill on a Monday(e.g.) should not have to wait a week or even a fortnight to see a doctor.
In my case it is even more worrying as it was the GP who requested an appointment.