If you have—as I can just about remember having as a child—a GP who you see every time you go to the doctor, then you will, almost by necessity, develop a relationship with this doctor. There is a chance that this could be a negative one. The doctor could get a certain idea in their head about you: if the first time you went to them you came in very worried about something which turned out to be inconsequential or a non-issue they might tag you as a hypochondriac. It makes you to some degree subject to them outside of each individual interaction.
The shift in the system to the "you will never see the same doctor twice" that seems to have happened in the NHS over the last 10-15 years does ameliorate that specific problem. If one doctor has a certain opinion of you, don't worry—you will almost certainly never see them again. You don't have to fret about them leaving them notes about their opinions in your file either, as the only thing that's less likely than you seeing the same doctor twice is any doctor reading the previous one's notes.
The problem is, though, that while your interaction with any given doctor may be good or bad, you no longer have any level of personal relationship with them. As a child, I had Dr Bainbridge, who seemed stuck in a perpetual state of being 50something, pretty much from as early as I can remember, all the way to my late teens, but he remembered me, he knew what my deal was, I felt like I had some kind of relationship with him. I've been with my current GP's surgery for nearly four years, and I think I've seen the same doctor there maybe twice, at a half-year remove? All the doctors are lovely but my relationship is not with them, it's with the system.