During my time having school medicalsin the uk (the vast majority 1960 - 1970) boys always had to get undressed / dressed in front of someone. There was a slight variation when younger at junior school (7rs - 11 yrs). I have posted in some detail on other related topics. So, here is an overview.
Junior School. Quite often, there was no dedicated medical room. At my particuar school (& many others I am sure). Boys' Medical Examinations took place in the school hall. About one third of the hall was screened off and the doctor & the school nurse were behind there.
Meanwhile, a whole class of boys (about 23 in my case) would be sent down to the hall, taking a library book / reading book with them. There were wooden PE benches set out. The supervising teacher (female more often than not) would tell everyone to take all of their clothes off - apart from underpants and vest fold them neatly and either put them behind or under the bench. We were then supposed to sit in silence and read until our name was called out (always in alphabetical order ) to go and see the doctor. Some boys did not wear vests and so were stripped down to just underpants. So, you always undressed in front of the teacher and each other.Not good if you were very modest or shy. Moreover, the hall was a thoroughfare and was not closed off. So you could be undressing (& later just sitting in your underpants etc while secretaries / caretakers / delivery people / class monitors (often girls) / whole classes of children etc were pasding through. A lot of people inevitably looked at you. At tbe end of the exam, you walked back across the hall and sat down again. When everyone had been examined, we were told to get dressed - again under supervision.
The medical part - into the nurse's area first. She would do several basic checks (scalp, nails, general obs, height / weight etc) then send you through to the doctor. By the end of his examination you would be naked. Now, maybe this was to save a little time, I don't know - but we were told to pick up our underwear and get dressed in the nurse's area. So, the nurse always briefly saw you in the nude. Moreover, as one boy cane out, the next was sent in. So, one of your classmates saw you naked - and, if you were the one going in, you always saw another boy briefly naked.
It was different at Grammar School (11 yrs - 18yrs). No mass examinations there. The appointments were all individual. Examinations took place in the temporarily converted Deputy Headmaster's office. You had to sit on a chair in the corridor outside. This time when you were called in, the previous boy came out wearing full uniform. The school nurse now told you to undress / take your clothes off - apart from vest / underpants. They were very authoritative and would be strict about making you fold your discarded clothing neatly.
The rest was virtually identical to Junior School. You still had to return to tbe nurse's area, naked, to dress. They might be filling in forns or getting ready for the next boy, but they would look at you. Often they were telling you to hurry up. I well remember a couple of times trying to go as fast as I could to get my underpants on that I would get flustered, put both feet through one leg hole, then overbalance etc. Thus, having to take my pants off and start again!! It was such a relief to be fully dressed and then sent out!!