There are rumours and allegations that he was a necrophiliac. His psychological profile certainly suggests that it is a possibility. Watch the Louis Theroux clip about Jimmy Savile. While talking in the back seat of a car, Saville says he has never had a relationship ever. And he absolutely has no feelings for anyone. To stop himself from getting hurt. That is a red flag for a necrophiliac.
Jimmy Savile was known for his charity work. He also volunteered as an hospital porter on the nightshift!
This has led people to speculate that he fucked dead bodies in the hospital morgue.