Or at least played one on TV!
After Kay wakes up at the end of the series, he gets a final glimpse of the two clergymen who, in his dream, were cast as Those Two Bad Guys. Evidently they're just innocent clergymen, travelling to Tatchester Cathedral for its 1000th Christmas service...or are they?
As Abner Brown would shout, "LOOK MORE CLOSELY!" One is shortish and plumpish with a neat, dark moustache; the other is lanky, beaky, and fair-haired. Add that we're in mid-1930s England, and what's the obvious conclusion? They're Hercule Poirot and Captain Hastings, in disguise as clergy to investigate strange goings-on at the cathedral. And since Poirot only rarely uses disguises, this must be, in his words, "a case of the most mysterious".
Tenuous, you say? Then how do you explain that The Box of Delights is directed by Renny Rye, who directed numerous episodes of the Poirot series?!