The paperback whose cover is illustrated above first came out in 1972, followed by three other volumes of non-Sherlock detective stories written during the same period. Edited by Hugh Greene, brother of Graham Greene, the books were a revelation to me. I started Reading Richard Austin Freeman’s Dr. Thorndyke stories; Ernest Bramah’s Max Carrados stories (Carrados was blind, and could read the London Times by feeling the elevation of the ink on the paper); the novels and stories of the vastly underrated Arthur Morrison; Jacques Futrelle’s “Thinking Machine” stories (Futrelle died on the Titanic); and Baroness Orczy’s The Old Man in the Corner Stories.
And that was only the beginning! I also noticed that the Victorians and Edwardians wrote excellent horror stories as well, and that many of them were available from Dover Publications, including such luminaries as Algernon Blackwood, M. R. James, Arthur Machen, Mrs. J. H. Riddell, and Wilkie Collins. Now, in the age of the Kindle and other e-books, one could pick up virtually all of Blackwood’s short stories in two “megapacks” for a mere $1.98. There are even two well-known “psychic detectives” investigating hauntings and possessions, namely Algernon Blackwood’s John Silence, the self-styled “psychic doctor,” and William Hope Hodgson’s Max Carnacki, the ghost detective.
The stories are, for the most part, available readily and inexpensively now that their copyright protection expired years ago. It may still be difficult to find some Arthur Morrisons such as the Martin Hewitt detective stories and the stories in The Dorrington Deed-Box.
Even G. K. Chesterton got into the act somewhat later with his Father Brown stories, which are in a slightly different vein, but which owe much to Arthur Conan Doyle and his “rivals.”
A good way to start is to find Hugh Greene’s collections on eBay or Amazon.Com and, if you like them, dig around in used book stores, or, if you are on a budget, Amazon Kindle and its “rivals.”