I was either 15 or had jut turned 16 the last time a parent was with me. However, my mother tended to make my appointments until she retired, as she worked at the practice. This meant that only the four GP partners could access my records, and the receptionists couldn't even find my name on the list of patients (it was kept off for confidentiality reasons).
The last time a parent accompanied me, I was 24, as I was particularly lethargic and not able to do much on my own. That time though, my mother sat and chatted to her colleagues in reception whilst I went in with the doctor alone.