This reminds me of another British film, that I cannot recall the name of. It's animated, and is about an old couple in the countryside. Unlike Threads, it's centered on these people, and they do their best to follow the instructions from the radio. You only get very slight hints that something is going wrong, like all the protractors suddenly going out of stock. And once the fallout happens, you watch as this charming couple, who are so good mannered that they keep trying to make each other happy through the fallout, slowly starves to death. It's very similar to Grave of the Fireflies, but while in that movie you can be put off by the elder brother's retarded decisions, this movie is absolutely bleak and very effective.
Edit: The movie is When the Wind Blows. Someone already recommended it above while I was typing this lmao