The Story of Lucy Gault impressed me so much that now I pick up this author's books whenever I find them, so I picked up Felicia's Journey by William Trevor without looking at anything but the author's name. This novel is about a serial killer, but there are no police, no investigation, no blood, no crime scenes... It seems atypical of books about serial killers. It's not a mystery or a crime novel. I'd say it's more of a psychological revelation, a real page-turner. It won the 1994 Whitbread Prize.
The back of the book contains reviews instead of the more usual synopsis/lure, but the Wikipedia page sets up the plot this way:
The plot follows eighteen-year-old Felicia, a poor provincial Irish girl, who was made pregnant and abandoned by Johnny Lysaght, a young man who is supposedly working in the English Midlands. Felicia's father believes Johnny has run off to join the British army. As Felicia journeys to the Midlands in search of the father of her unborn child, she meets with mild-mannered Mr Hilditch, the manager of a catering companyThere's a reading group guide online here. The Independent calls it "as harrowingly grim as anything fictional you'll read this year." Kirkus Reviews closes by saying, "Trevor's combination of the pathological and the lyrical transcends mere genre fiction: He's a master still exploring the possibilities of his craft."