The Affacombe Affair by Elizabeth Lemarchand

Affacombe is a picturesque English village, sleepy and traditional, populated by the usual cast of characters - the retired Colonel and his wife, the scholarly vicar, the lady historian/writer, the blunt and bossy spinster with her fingers in all the church pies, the gossipy pub-keeper.

And a quiet, neat, and very efficient blackmailer, with a long history of successful low-level extortion. When her body is found in the river, it's up to Detective Inspector Pollard and Sgt Toye to decide which of her victims is the guilty party. But as Scotland Yard tries to build a case against a series of unshakeable alibis, someone's story starts to fall apart at the seams.