ladyalex....this is socialised medicine.......the doctor needs time off, holidays and sometimes he is even sick, so continuity of service, although desirable, is not always possible. The popular doctors, for whatever reason, have long waiting lists and so if you want to see the popular one....you have to wait.
In hospitals it is exactly the same, the Consultant can´t see all the patients at his clinic and so "dishes" the case notes out to his juniors.
If a GP or Hospital doctor was paid for each patient he saw and each operation that he did, then the doctor would be more likely to see "his" patients, but that is not the way it works. The NHS will guarantee that you see "A" doctor, but cannot guarantee the quality.
Now if you want continuation of care ...... same doctor.....always the Consultant and not his junior, then you have to go Private.