From Wiki:
"Lady Jane" was written and composed by Jagger in early 1966 after reading the then controversial book Lady Chatterley's Lover, which uses the term "Lady Jane" to mean female genitalia. According to Jagger, "the names [in the song] are historical, but it was really unconscious that they should fit together from the same period." At the time, it was widely thought that an inspiration for the song was Jane Ormsby-Gore, daughter of David Ormsby-Gore, former British ambassador in Washington, who later married Michael Rainey, founder of the Hung on You boutique in Chelsea that was frequented by the Stones.
"As we say in England, it can get a bit trainspottery"