Each of Sky Arts' Urban Myths has had a different tone and this one is no exception. Agatha Christie delves into the mystery surrounding the12-day disappearance of the celebrated crime writer in 1926. This is an that really happened and nobody quite knows what happened. Christie certainly never shed any light on her unusual behaviour.

In this elegant production directed by Guillem Morales, who has worked on some of the best Inside No. 9's so has a great track record at making short self-contained stories, Anna Maxwell Martin plays the writer, but, as the plot dictates, she soon disappears. Instead we follow fellow crime writers Arthur Conan Doyle and Dorothy L Sayers as they play detective and look for clues.

Bill Paterson's Sir Arthur Conan Doyle is the more famous and is grandly dismissive of Sayers (Rosie Cavaliero), expecting her to fetch and carry for him and make tea. And when she does have a good idea about the case – and she has plenty – he tends to claim it for himself. And when Conan Doyle isn't being chauvinistic he is wondering if the spirit world can help him out. Nick Mohammed chips in as a mentalist looking for clues beyond the grave. Not that Chrostie is beyond the grave, despite Conan Doyle's guess work.

The cast is certainly a starry one, with Mark Bonnar as Christie's agent and Adrian "Miranda and loads more stuff" Scarborough also pitching in as Conan Doyle rounds everyone up for a Sherlock-style showdown. Inevitably while Conan Doyle is well wide of the mark Sayers cracks the case, tracking Christoe down to a Harrogate hydrospa where she is serenading guests in the dining room. It would be criminal to miss this.

May 17, 9pm, Sky Arts and available to Sky Subscribers now.