The Crown
 

In the episode 10 of season three of the Netflix series "The Crown," in what is apparently a (somewhat) true story, Princess Margaret discovers that the boy toy she has her eye on, Ray Llewellyn, does not have swim trunks to join the pool party. They go to the nearby town to procure a suit for him. This is 1973 and briefs are plentiful at the department store. Llewellyn picks a green brief, but the princess opts instead for a Union Jack brief, then insists that he try it on and model it for her. There are several scenes in the episode with him in that and other, relatively brief, suits. Though the actual suit they bought that day is not known, the real Llewellyn appears in an iconic picture at Margaret's Caribbean estate, Mustique, wearing a Union Jack brief
https://www.dailymail.co.uk/news/art...fee0a854214f69

Here is a link to an image of the show.

https://www.imdb.com/title/tt4786824...ame&ref_=tt_ch

I think the cut is correct for the early seventies.
Thinner sided briefs only became popular a few years later when proper stretch nylon appeared.