The Real Inspector Hound opens with two theatre critics, Moon and Birdboot. Since Moon's superior, Higgs, is unavailable, Moon is called upon to review the production. The other critic, Birdboot, seems to have an interest in the young actress playing Felicity Cunningham. Birdboot states that he is a "respectable married man", yet Moon's comments direct the audience to doubt this statement.
The play within the play is set in "Lady Muldoon's country residence one morning in early spring" and opens with a body lying on an otherwise empty stage. The help, Mrs. Drudge, gravitates to the radio, oblivious to the corpse, and turns it on just in time for an overly expository police message explaining that police are searching for an escaped madman in the swamps surrounding the manor. Simon, a mysterious young man new in the neighbourhood enters the house, and it is revealed that he has dumped Felicity Cunningham for her friend Cynthia Muldoon, lady of the house. In the audience, Birdboot has mentally done the same. Major Magnus Muldoon, Cynthia's brother-in-law, is also in love with Cynthia. Eventually Inspector Hound from the police force arrives on the scene, apparently searching for the madman, and the company finally notices the body. The company splits up to look for a man of suspicion, when Simon is left alone on stage with the body, he bends over it and seems to recognise the victim, at which point he is shot by an unknown assailant.
During the play the two theatre critics discuss things they may write about this typical whodunit, but they are often sidetracked by their soliloquies, Moon's concerning his professional jealousy of Higgs and Birdboot's concerning his newly found "love", the actress playing Cynthia. As they talk, the telephone on stage begins to ring incessantly until Moon cannot stand it any more. He walks up on stage to answer it only to discover that Birdboot's wife, Myrtle, is on the line. Birdboot speaks to her and as he hangs up, the play suddenly starts again and he gets trapped in it, mistaken for Simon, leading to his inevitable demise as he executes the role to its end, just after recognising the dead body onstage as Higgs, the first string critic who was unavailable that night. Moon ascends the stage to unravel Birdboot's death, taking on the role of Inspector Hound. Major Magnus accuses Moon of being the madman, since he is not the real Inspector Hound, and he tries to run but Magnus shoots him. As Moon lies dying on the floor, Magnus reveals himself to not only be the real Inspector Hound but also Cynthia's lost husband, Albert, who had disappeared ten years earlier. Moon, however, also recognises him as third-string critic Puckeridge, who will now become the first-string as both Higgs and Moon are out of the way.