Hancock lost her necklace in the Haymarket area in London and is asking anyone to look out for it if it is found or offered to dealers or auction houses for sale.
The actress said the gold chain held her father's signet ring, her mother's wedding ring plus her wedding rings with her first husband Alec Ross, and her second husband John Thaw.
Anyone with information should contact @4SheilaHancock via social media.
Separately, police are appealing for information following a burglary of a 91-year-old woman who was robbed in her Beckenham home.
The victim was at home on the afternoon of June 27 when two men knocked on the door and pretended to be there to repair a leak in the boiler.
While she was distracted they conducted a search of her home before fleeing, having stolen jewellery including a locket. The locket had been given to the victim by her parents on her 18th birthday and included pictures of her late mother and father. A number of bracelets were also stolen.
Det Sgt Sarah Francis, said: "This horrible ordeal has left this elderly woman feeling utterly helpless.
"The stolen locket especially is of enormous and irreplaceable sentimental value. I urge any local people, or jewellers, who may have been offered such an item for sale, to please contact us immediately."
The police have released E-FIT images of two suspects (pictured here).
Anyone who has information that could help police should call 101 reference CAD 5016/27JUN or contact Crimestoppers anonymously on 0800 555 111.