Dark comedy by AL Kennedy, set in 1870s London and based on a true story.
Mr Parker is a sincere and kind man who, in search of a higher meaning to life, has moved from conventional religion to seances and spiritualism. He believes he has met his saviour in the guise of Mr Thomson, a charming, erudite and utterly mesmerising medium. But, unbeknown to Parker, Thomson is a complete and utter fake.
Part of the interest is that the play is a historically accurate take on the adept magicianship used by mediums in the Victorian era, the heyday of elaborate physical mediumship. The origin of the "true story" isn't identified in any of the schedules, but from the title I'd guess it drew on the anonymous 1882 account Confessions of a medium (Internet Archive confessionsofmed00londrich). The mechanics of spiritualism by Harry Price ("the first celebrity ghost-hunter") has a number of other accounts and titles such as Revelations of a spirit medium (Internet Archive revelationsofspi00farriala), which caused a sensation on its first publication in 1891. Price writes:
... the work itself is a brilliant and detailed exposé of most of the tricks used by fraudulent mediums, who bought up all the copies they could find and destroyed them. The book is now of the extremest rarity. During a lifetime's collecting of rare books on magic I have found only three copies. One of these I sacrificed in order that a facsimile edition could be produced by the anastatic process 1
Parker and Thomson in the radio play appear to have been inspired by the partnership of Douglas Blackburn and George Albert Smith, who had a similarly ambivalent relationship over whether what they were doing was fraud. Their telepathy double-act even managed to get accredited by the Society for Psychical Research; some years later Blackburn, thinking Smith was dead, revealed how it was done; but Smith turned up and denied it. See the Blackburn and Smith entry in James Randi's An Encyclopedia of Claims, Frauds, and Hoaxes of the Occult and Supernatural. The story is covered in some detail under Confessions of a "Telepathist" on pages 114- in Journal of the Society for Psychical Research for Ocotber 1911.
1. Anastatic printing produced a facsimile by destroying the original. I'm not sure what was up with just copying out the text.