The Nice And The Good by Iris Murdoch
A revolver shot rings through a Whitehall office one hot afternoon in the middle of an English summer. A Government official has apparently shot himself, but the circumstances are questionable - prompting Octavian Gray, head of the department in which the dead man worked, to investigate.
Lawyer John Ducane is charged with the task, interviewing other civil servants by day, and by night attempting repeatedly - and unsuccessfully - to break up with his mistress. When Ducane travels to Gray's Dorset home everything becomes even more mysterious and nothing is quite as it seems.