The inaugural post on this thread
www.zity.biz/index.php?mx=forum;ox=display;topic=23360.msg228380#msg228380
describes an examination close to the one mentioned (same age/year) though the girl was not naked, it appears she could have been if she'd accepted the invitation to be examined further - assuming she didn't put her bra back on.
I've collected quite a lot of information over the years about UK school medicals. I have to say this one is something of a rarity in terms of the level of undressing as applied to girls. Even in the 60s and 70s, a typical scenario for teenage girls would have them removing their skirt and bra, and putting their blouse back on before they went in front of the doctor, they would then open the blouse for stething. Girls didn't usually have a genital examination beyond a quick look down their underwear, so were not usually required to strip completely.
Boys, however, did usually get a genital exam, and as such would either end up naked or with their underpants pulled down. As can be seen from many posts on the subject on the Forum here, it was not at all unusual for boys (regardless of age) to be told to by the nurse to strip naked at the start of the exam (happened to me twice), and so would be weighed and measured (and even have to do the eye test) naked.
Back then there certainly wouldn't be any question of being asked if you wanted this test or that (as mentioned in the account on the other thread), they just did what they wanted to you with no explanation, and not so much as a "please" or a "thank you"!
Medicals done this way started to peter out in the early 80s (though I have read of some being done in the 'old-fashioned' way quite a bit later than that) and they were no longer universally applied. It was judged that the number of faults identified (around 2%) did not justify the use of resources: parents were asked to complete health questionnaires instead, and only those who were thought to be susceptible to some ailment or other were actually examined.
Having said that, I think Scotland went its own way and continued with the universal system. I can't imagine any school or school clinic using today the methods that were employed in bygone times. No one thought much of it at the time, it was accepted practice and wasn't questioned. Many people find it hard to believe that such things went on - rather like the use of corporal punishment - and there was so little concern for children's modesty, especially that of boys - bear in mind, most paediatricians in those days were women, and the nurses were always female.