A Shilling for Candles (Musaicum Vintage Mysteries). Josephine Tey

The body of a film actress known as Christine Clay is discovered at the edge of the surf on a beach in Kent. She is initially thought to be the victim of a drowning accident, but the presence of a button tangled in her hair leads Inspector Alan Grant to conclude she has been murdered. Suspicion quickly falls on her friend and house guest, Robert Tisdall. Tisdall was rescued from a life of poverty when Clay randomly encountered him in London and offered him hospitality out of kindness. The day before the murder, Clay wrote to her lawyer instructing him to add a codicil to her will bequeathing a small portion of her estate to Tisdall. This is strong evidence against Tisdale, but Inspector Grant's intuition urges him to keep investigating. As more clues are revealed it becomes clear that more than one people wanted young actress dead and could have a benefit from her death.