If it did really occur, the romance between the royal figure and the flamboyant thug was short lived, taking place during a few weeks in the Caribbean at some point in the mid 1970s. After her marriage to Lord Snowdon fell apart, Margaret was something of a party animal and supposedly slept with a number of famous people, including Warren Beatty, Mick Jagger, Peter Sellers and David Niven. Bindon wasn't as much of a celebrity, but the sometime criminal -- and future murder suspect -- had been in movies since co-starring in Ken Loach's 1967 drama Poor Cow.
His affair with the princess has been fodder for film before. Last year, UK's Channel Four aired a documentary titled The Princess and the Gangster featuring dramatizations of the alleged events. Less direct, The Bank Job involves a safe deposit box containing photos of Margaret in a threesome including Bindon (his name was not mentioned, however). According to Bindon's Wikipedia page, he was the inspiration for Vinnie Jones' character in Lock, Stock and Two Smoking Barrels. Perhaps Jones could therefore take the lead in this film?
Princess' Gangster somewhat reminds me of the affair between actress Lana Turner and gangster Johnny Stompanato, only on a smaller, less violent level. A movie portraying that story had been in the works for a number of years with Catherine Zeta-Jones and Keanu Reeves set to star, but the project was apparently canceled. So the Margaret-Bindon tryst may be a fair substitute, even if it the princess doesn't murder the guy at the end of the second act (as Stompanato would have).