The Lighthouse is 13th in the P.D. James Adam Dalgliesh mystery series. An excerpt can be read at her site. I've read several in this series and always enjoy them.
from the book jacket:
Combe Island off the Cornish coast of England has a bloodstained history of piracy and cruelty. Owned for centuries by the same family, it now serves as a place where over-stressed men and women in positions of high authority can come to find serenity in conditions of guaranteed security. But when one of its distinguished visitors is found hanging from Combe's famous lighthouse, an apparent murder victim, the peace of the island is shattered.
The situation is awkward, demanding exceptional skill and discretion on the part of investigators. Commander Adam Dalgliesh, well known and admired for exactly these qualities, is called in to solve the case. Unfortunately, it is a difficult time for the Commander and his team. Dalgliesh himself is distracted, uncertain and deeply worried about his future with Emma Lavenham, the woman he loves; Detective Inspector Kate Miskin is coping with tenacious emotional problems of her own; the ambitious Sergeant Francis Benton-Smith is not happy about having a woman as his superior. Moreover, the team has scarcely begun to unravel the motives of the various suspects before a second brutal killing occurs. Then, as if to challenge them to the utmost, a new and unexpected - and deadly - threat suddenly confronts Dalgliesh personally, leaving Miskin and Benton-Smith to carry on alone in a race against time.
A richly complex tale of crime and passion, The Lighthouse is a deeply satisfying novel, P.D. James at her masterly best.
The Guardian has a positive review of this particular work and good words about the author. Kirkus Reviews also likes it.
I have blog posts on these:
#2 A Mind to Murder
#5 The Black Tower
#7 A Taste for Death
#9 Original Sin
#12 The Murder Room
and An Unsuitable Job for a Woman, which features an appearance by Dalgliesh.