Frist of a four-parter here, with episodes of the Star Trek Original Series that were deemed unsuitable for audiences by the BBC. While each has their own "offending" themes and scenes, the core of the problem was that the UK broadcaster thought of Star Trek as a children's show, and would thus screen it for anything it felt too mature a topic.
Easily the tamest of the four is Miri, a Season 1 episode that sees the crew encounter a Lord Of The Flies-inspired society comprised entirely of children. All the planet's adults have perished from some lethal, unknown plague, and the episode does throw in the odd violent scene, but besides that, there's nothing remotely troublesome from a visual perspective.
The problem with the episode though was it focused on large groups of orphaned children facing their deaths from either the virus that killed their parents or simply just starvation. The BBC insisted the episode didn't do enough to soften the edges of this grim subject matter and refused to show it.