I wasn’t delighted when I learned that Richard Osman was setting his Thursday Murder Club crew aside for a little while to write a new series. The adventures of Elizabeth, Ron and co might not be fiercely plotted, hardcore crime stories, but they bring a little slice of joy and warmth on a yearly basis. I needn’t have worried. Osman’s new series, which kicks off with this book, is written with just as light a touch and gently humorous tone.

Amy is a private security officer currently protecting Rosie D’Antonio, “the world’s bestselling novelist, ‘if you don’t count Lee Child’”. They’re on an exclusive island – a nice change for tough nut Amy, who, “for various operational reasons”, once “had to spend the best part of a month living inside an abandoned oil pipeline in Syria”. Amy’s father-in-law, Steve, with whom she regularly talks on the phone (the deep and understated love between them pair is the beating heart of this novel), is a widower and retired police officer, living in the New Forest and regularly noting strange goings-on on his dictaphone. “Steve hadn’t been hoodwinked by the hollyhocks and the cupcakes and the cheery ‘Good morning’ greetings,” writes Osman. “Steve had seen secrets behind every pastel front door, seen corpses in every back alley.”

When Amy is lined up as the fall guy for a string of murders, she and Rosie go on the run, a killer on their trail. What do Amy’s suave boss, Jeff, and his former partner and best friend, Henk, know about the situation? Did Jeff survive an attempt on his life? What’s going on in Letchworth Garden City, and will an adorable wannabe influencer (Bonnie is trying to make it in the cut-throat world of paint influencing) be the next victim?

Steve, a no-nonsense man who says things such as: “I don’t have sunglasses… I’m not a male model”, isn’t keen on being swept up in the death and destruction that has begun following Amy around. But he’ll do it for her. He might even get on a plane, though “hopefully they can wrap this all up before the quiz night next Wednesday”.

The plot might get a little meandering, and I’m not sure I cared all that much about discovering the identity of the main villain, but that doesn’t matter, because it’s so much fun travelling the world with Amy, Steve and the fantastic Rosie. Even Osman’s minor characters are exquisitely ridiculous – from terrible actor Max, who “if he ever sees crying in a script, makes sure they change it to ‘a roar of anger’, which he can do very well”, to uptight Dutchman Henk, who makes sure everything is accurate at all times: “It is not a little envelope, it is an A4.”

The thing that shines through in Osman’s writing, for me, is that he really likes people and revels in all their foibles and eccentricities. All of which makes for a delightful read – and another little slice of warmth in time for autumn.

• We Solve Murders by Richard Osman is published by Viking (£22). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply