AI says this:
This is almost certainly the standard school entry medical examination, run by the NHS School Health Service, which was routine (and effectively compulsory) for children starting infant/primary school in the UK right through the 1980s.
• Structure: it was a one-to-one appointment, not a group check — a school doctor (often called the “school medical officer” or a clinical medical officer) did a full paediatric exam, with the school nurse assisting and doing preliminary measurements. That’s why it needed forms, took ~30 minutes, and happened outside normal group activities. The examination included a parental interview, growth and visual acuity measurements, and a hearing sweep test carried out by the school nurse, plus a paediatric examination and neurodevelopmental assessment carried out by the school doctor.
• Parent present: standard practice — parents were invited/expected to attend, especially for the youngest children.
• The physical exam, including genital check: this was routine, for both boys and girls, as part of the standard paediatric exam — checking for things like hernias, undescended testicles, hip problems, or other physical abnormalities.
• “I can see you through this little hole, you can’t see me”: this sounds like part of a vision test — a pinhole occluder is a real, standard optometric tool. Vision screening for young children in this era used tests like the STYCAR system, which involved matching shapes/letters at a distance and various occluder tricks to test each eye separately or check acuity — dressed up as a game for a small child.
So in short: it wasn’t one specific mysterious event — it was the routine “school entrant medical,” standard practice across the UK from the early 20th century up until it was scaled back/phased out through the 1990s (partly for cost reasons). The fact that it was 1-to-1 with a parent present, involved forms, took half an hour, and included a full physical + vision/hearing screening is very consistent with this rather than an ad hoc or unusual exam.