This was the first of Dorothy L. Sayers' detective novels, but 70-odd years after publication it's not the best introduction to Sayers or to her most successful hero, Lord Peter Wimsey. If that's what you're looking for, try Nine Tailors, Murder Must Advertise, or one of the books that include Harriet Vane (my personal favourite is Gaudy Night).
"Whose Body" is something of an apprentice work. Lord Peter is here more a bundle of characteristics than a character: a collector of rare books and incunabula, facile with quotations, fluent in French and probably in Latin, a skillful and sensitive pianist who never needs to practise, slightly built but possessed of "curious" strength and speed which he maintains without exercise. Over subsequent books, this caricature smooths and deepens into one of the most interesting and attractive detectives in fiction.
In spite of its awkwardness, Whose Body is worth reading. The plot is clever, the villain is believable and sadistic, and most of the supporting characters are a delight. Some of these characters are further developed in later novels: Bunter, Parker, the Dowager Duchess, Freddy Arbuthnot. Others fortunately are not. Sayers is much better with people she might recognise as "like us" then with people from other social groups.
Sayers developed into a powerful writer of fiction whose technique was imperceptible. Here she has less mastery of technique, so that the scenes that work have disproportionate impact. The encounter between the Dowager Duchess of Denver and the American millionaire Milligan is a tiny classic.
In summary, interesting and entertaining for existing fans, but a hurdle for newcomers to the world of Wimsey.