Despite being given the name of "the Grey Lady" this ghost has nothing to do with either Lady Jane Grey or her family.
Mrs. Sibyll Penn was the nurse of Prince Edward and even had her own lodgings at Hampton Court (see the tour of Hampton Court Palace). When she died of smallpox in 1562 she was buried in the St. Mary's Chapel and rested peacefully there until a storm destroyed the chapel in 1892. Her remains were therefore removed which is thought to have called her back to the palace in which she used to live and work.
Residents and craftsmen working on the palace have reported hearing a strange sound which they identified as the sound of a spinning wheel turning. When a wall was removed an hitherto unknown chamber was found - and there was indeed a spinning wheel worn down by continuous use! Apparently, the spinning wheel belonged to Mrs. Penn and the room in which is was discovered also happens to be the rooms of the former nurse.
Many visitors have seen her before and after the discovery of the room. Out of all the ghosts at Hampton Court Palace she is the most persistent. She was spotted in person in 1986 and is said to appear in different courtyards and rooms - at times watching over children who visits the castle.