The Safety Pin by Joseph Smith Fletcher

An elderly man called Deane is murdered in an English town. Inspector Mellapont thinks it's a simple robbery, but others disagree, and Deane's business partner, an attractive young girl named Miss Pretty, offers a reward for information. No fewer than three rogues decide to improve their own prospects by investigating — the two Hackdale brothers, John and Simmons, working independently, and the town drunk James Bartlett, who sobers up rapidly when blackmail and extortion are in prospect. Attention centers on the mayor, Mrs. Champernowne; but when thieves fall out information gets into the hands of the police and a local solicitor, Francis Shelmore, and the plot unravels rapidly.