Obviously, The Prince and the Showgirl, referred to as The Sleeping Prince in the film did happen. However, whether the actual love scenes between Colin Clark and Marilyn actually happened is doubtful. The Prince, the Showgirl and Me was Colin’s first book which didn’t mention the weeklong affair.
So, later on, he used this for his “story”. Unfortunately, anyone who would’ve witnessed this never commented on it, have passed away or never saw any signs of this happening.