This book seemed like a mood piece; I felt as if I were in a boy's school town. Although the book took place sometime after World War II, things have probably not changed much in school towns in a hundred years.
The small town is at odds with the school; the folks at the school follow Church of England while the townsfolk are all Chapel. The murdered woman didn't really fit in; she was the only person from the school who went to Chapel.
George Smiley, the retired spy, is given an entry into the town by grace of his friendship with the brother of one of the school dons. The police can't get a word out of the school folks (they are a closed society) and the police are glad to have Smiley do some gentle snooping for them.
Le Carre weaves a delightfully devious plot, with twists and turns aplenty. Watch a master of the genre at work. Enjoy.
George Smiley Series
A Call for the Dead (1961)
*A Murder of Quality (1962)