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When American Simon Wells tries to pick up an attractive woman named Joan on the promenade at Weymouth, he is robbed and beaten by a motorcycle gang. Bernard, a scientist, and his friend Freya, a sculptress, come to his assistance. Later, Simon meets Joan again and learns that she is the sister of King, the leader of the motorcycle gang. She and Simon hide from King in Freya's studio, but he finally locates them, and as they attempt to run away, all three fall from a cliff into the sea. A group of strange children rescue them and take them to a cave, where Simon and Joan discover that the children belong to Bernard's secret research project. Exposed to radiation before birth, the children are now capable of surviving in a radioactive atmosphere in case of nuclear war; they have been kept completely isolated from the outside world, cared for and educated by automation. King is antagonistic toward the children, but Simon and Joan decide to help them, not realizing until it is too late that the children are radioactive. As Simon and Joan attempt to lead the children out of the cave, they are intercepted by soldiers under Bernard's direction. King tries to escape with one of the children, but after the child is recaptured, King's car goes out of control and plummets off a bridge. Bernard then allows Simon and Joan to escape in a boat, knowing that they will soon die from exposure to the intense radiation. Meanwhile, Freya has also found out about the project, and Bernard is forced to kill her and seal the children inside the cave.