I grew up in the Midlands and got examined at 5 and 16. Both times the
routine was to be ordered by the nurse to strip naked at the start of
the exam and have height and weight taken by her, then the doctor
(female) would do a head-to-toe examination: hair, scalp and nails;
ears, nose, mouth and teeth; heart and lungs checked with stethoscope;
joint mobility; test for hernia; penis and testicle inspection.
You are right that the exam format varied from area to area, and from
school to school. I never had the 'pleasure' of having to visit our
local school clinic, but it had the same reputation as yours seemed to
have: it seemed almost whatever you went for you ended up minus most, or
all, of your clothes! I'm sure that would have been the case for a full
medical.
One thing that also seems to be common experience is that girls didn't
get examined as thoroughly as boys, or have to undress completely -
despite the fact that the doctors usually were female.
I did hear tales about erections being 'subdued' in the way you describe
(I never knew whether to believe them), I don't really see why they had
to do that as it wouldn't have really interfered with the examination:
things sure were different then, such action would be regarded as
assault now.
Just out of interest: you say you only had to strip to the waist; was
this the case at all the exams you had? Was there not even a hernia
check?