The Weathermonger by Peter Dickinson

Geoffrey wakes up on a rock in the middle of the bay, with no memory of the past five years. His sister, Sally, tells him that he is the town’s weathermonger; he has the power to change the weather. England has reverted to the middle ages, and machines are regarded as witchcraft. The townspeople discovered Geoffrey trying to fix a motorboat, and are drowning him and Sally as witches. Geoffrey makes a fog and they get away in the very motorboat he had been trying to fix. They go to France, which remains unchanged, and are almost immediately sent back to steal a Rolls Royce and try to find the source of the spell.