Rivers of London (UK)
Midnight Riot (US)
Rivers of London is an urban fantasy/mystery novel set, as you may have guessed, in London. The story follows Peter Grant, a young probationary constable on the London police force. He isn't actually a particularly good copper; he's competent, certainly, but he's more interested in history and architecture than keeping an eye out for rowdy drunks. Once his probationary period is up he is expecting (but certainly not wanting) to be assigned to a boring desk job. Then he meets the ghost.
The ghost is very spooky and all, but this is overshadowed by the fact that it was the witness to a recent murder, so Peter interviews it. The ghost has some actionable intel, which leads to a sticky problem... How do you report that your witness is dead, no one else can see him, and you yourself might not be able to contact him again? As it happens, the London PD has a procedure for that.
Specifically, you are contacted by an enigmatic but dapper middle-aged gentleman and tested for uncanny abilities. And then put on special duty, dealing with This Sort of Thing so that the rest of the world doesn't have to. Peter finds himself the low man on the totem pole when it comes to dealing with river spirits, vampires, ghosts, and a rash of psychopathic demonic possessions that causes Londoners to commit violent murders and then explodes their faces.
While my writing style may not communicate it well, this is not by any means a light comedy; while Peter has a good, if dark, sense of humor, the story contains a fair amount of gore and violence (not limited to the whole 'exploding faces' thing). Peter is very much a cop, and we get to hear lots about proper policing technique and life on the force. We also get to hear lots about England's history and architecture, which is more interesting than it sounds. The result is an intelligent police procedural with magic and monsters, and one of the best urban fantasy stories I've read.
Rivers of London is the first of a series that is alternatively referred to as the Peter Grant series or the Rivers of London series. The next book in the series is Moon Over Soho. There are currently six books in the series, each as good as the last.