On the BeachHaven't seen this old 1959 film but it was recommended by someone on Jay Hansen's War Socialism list, and it won some Oscars too.
Someone, somewhere, pressed the button and started World War III. Australia has survived - temporarily. The radiation is on it's way, the end inevitable. This is the story of the way in which people faced the coming end, focusing mainly on a young Australian couple and their friends, including the captain of an American submarine that was on patrol in the Pacific when the bombs were falling. And then the Australians detect a morse signal coming from somewhere around San Diego..
Given that nuclear war is becoming a bigger threat again I think it would be good to show some nuclear films - eg. Threads too, which is set in Sheffield.