Pevensey Castle stand on what was once a peninsula projecting from the Sussex coast. This site was first fortified by the Romans, and was where the Norman Conquest of England began, when William the Conqueror landed there in 1066. He built temporary defences at Pevensey and later a great medieval castle inside its walls.
The castle is reputedly haunted, by the wraith of a "pale lady" that watches from the upper walls. Some have suggested that this is the ghost of Lady Joan Pelham. There are also reports of the sounds of a battle heard in the vacinity of the castle according to Mason.
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For further information, please read Haunted Castles of Britain and Ireland by Richard Jones and Haunted Heritage by John Mason.