Remembrance of the Daleks - S25-E1
Corrected entry: We know the episode takes place on 23 November, 1963 because the first episode of Doctor Who is about to come on TV when Ace leaves the room. JFK was assassinated less than 24 hours ago, and nobody seems to be affected. Granted, the military characters have other things on their minds, but none of the civilians wear black armbands or even mention that the biggest news story of the year that just happened.
Correction: You said it yourself: the people have other things of importance to worry about. This is set in London, where the reaction would not have been as significant as in America. It is set in a school where the lessons would have gone on as normal. At most there would be some discussion in an assembly.