I read this one for Country House Murder, and it is a good example of that particular type of mystery. It would also work for Murder Most Foul and Amateur Sleuth.
The Crime at the Black Dudley is designated as the first of the Albert Campion mysteries, but as others have noted, his appearance is pretty minimal. The main character is Dr. George Abbershaw, who seems to be at Black Dudley primarily to cement his relationship with the adorable Meggie.
Shades of The Big Four, Abbershaw and his friends seem to have stumbled into some sort of an inexplicable criminal gang conspiracy involving a German man who is referred to as the Hun, who plans to set the place on fire and burn them up with it. The plot is bizarre, convoluted and somewhat incomprehensible. No one seems to be able to figure out why Campion is there or who invited him.
I am going to reserve judgment on Allingham and her detective, since I don't think that this book is a particularly good example of her work. As a country house mystery, it was just all right, no where near as good as The Mysterious Affair at Styles or Peril at End House. As a detective, Campion isn't flattered by comparison to Poirot and his leetle grey cells or Peter Wimsey and the fabulous Bunter.
The next book in the Campion series is Mystery Mile, but I'm wondering if I wouldn't be better off digging deeper into the series. Martin Edwards mentioned Traitor's Purse & The Case of the Late Pig in The Story of Classic Crime in 100 Books, and I've heard good things about The Tiger In The Smoke, so I'm thinking of trying one of those the next time I give Campion a try.