The second serial presented on Doctor Who, a six-part story called “The Daleks,” was set on a distant world where the nightmare of 1962 actually came to pass; two nations, the Thals and the Dals, had been locked in an arms race for some indeterminate period of time, finally developing nuclear weapons, resulting in a full nuclear exchange between the two and irradiating the planet Skaro. The radiation was so severe that by the time our heroes arrive, the forests are petrified and full of mummified animals. Those who survived the exchange are now drastically mutated. The Thals have mutated full-circle, becoming a handsome race devoted to peaceful coexistence. They believe the Dals are either extinct or so horribly mutated that they cannot emerge from their frozen city. Neither is completely true; the Dals have mutated horribly, to the point where they have no skeletons and are no longer capable of independent life, but they have developed tank-like travel machines, equipped with life support and a formidable weapons system. They have become the Daleks.
For more interesting Doctor Who plots that originated from real events, don't miss this great article on Mental Floss.