Fran Varady is one of the more unusual amateur sleuths I've come across. A would-be actress living mostly on the dole in London, both her hair and personality are spiky. Her friend Ganesh tries his best to keep her out of trouble, but seldom succeeds. In this, the second in the all-too-short series, she buys a cup of coffee for an alcoholic drifter and is plunged into a mystery. Ann Granger is better known for her Meredith and Markby mysteries, which are more traditionally "cozy." The Varady series has many cozy elements but with a young, urban twist that makes it a lot of fun to read.
What do You think about Keeping Bad Company (1998)?