There really is a book called "Lady Don't Fall Down Backwards", but its not a Murder Mystery, it's actually a true story about Joan Le Mesurier's affair with Tony Hancock. The title of the book is just a homage and there is even a cartoon on the back of Hancock in this episode.
The London City Council heritage plaque at the author's home reads: "D'ARCY SARTO 1884-1949 NOVELIST lived here".
Old Drum Lane is mentioned. Oil Drum Lane would become important to writers Ray Galton and Alan Simpson later; as it is the address of Albert and Harold Steptoe in Steptoe and Son.
There is now a real novella of the fictitious "Lady Don't Fall Backwards", published in 2021 by the similarly fictitious Darcy Sarto, lifted directly from references in this episode.