I don't think that's the case in the UK at all. Maybe in America, but in the UK, this event did not have the cultural resonance that it had in the US. Just because we know something, doesn't mean everybody or even the vast majority does.
Did you not go to school? If there are two names you should remember from being taught about the civil rights movement it would be Martin Luther King and Rosa Parks?
I was at school in the 70s, I don't recall being taught anything about civil rights etc, such things were kept brushed under the carpet
By the time I made it to school in the 90s it was considered history. Going way off topic but we seemed to learn far more about American political history than British political history. I think the UK history I was taught was basically 1066, Tudors and Stewarts, Queen Victoria and the two World Wars.