It has been five years since the award-winning Kate Atkinson last gifted us a Jackson Brodie novel, in Big Sky. Now her private investigator, who has “climbed to the wrong side of 60”, is back, and it is a real joy to see him again. Death at the Sign of the Rook (Doubleday) throws Brodie into the middle of an Agatha Christie-esque mystery when he is hired by elderly siblings to find a painting that has gone missing from their late mother’s wall. Brodie discovers parallels with the theft of a Turner painting from a nearby stately home. As he is wont to say, “a coincidence is just an explanation waiting to happen”, and he’s delighted to discover that old friend Reggie Chase, the orphan who saved his life back in When Will There Be Good News?, was in charge of that investigation. Reggie is less pleased – “we’re not a partnership, we’re not ‘Brodie and Chase, Detectives’,” she tells him – but they are soon back in harness when a handy snowstorm means they’re trapped in the stately home, along with a cast of vicars, butlers, majors, aged dowagers, etc, of whom Christie would be proud. An axe murderer stalks the moors, there’s a body in the pantry and a cast of actors on the loose.

This stands alone as a crime novel, but it is better enjoyed having read the previous books in the Brodie series. And why wouldn’t you, anyway – they are all a delight. I defy you not to snort with laughter as the novel progresses to its farcical denouement. Atkinson is just brilliant.

If you’re one of the many who love Mick Herron’s Jackson Lamb novels, but missed his previous series, starring the Oxford-based private investigator Zoë Boehm, never fear: the first in the sequence and Herron’s debut, Down Cemetery Road (Baskerville), is about to be adapted by Apple TV (starring Emma Thompson and Ruth Wilson). Handily, it’s being reissued by its publisher and is a not-to-be-missed treat.

This novel is less about Zoë than her partner, Joe, who is called on by an Oxford housewife, Sarah, to investigate when a house on her street explodes, killing two adults. Sarah becomes obsessed with what has happened to their young daughter, as no one else seems interested, and asks Joe to help. “I won’t lie. Philip Marlowe, I’m not. But who is? Most of what I’m hired to do, I manage,” he tells her. As they dig deeper, they discover all sorts of nefarious government goings-on (this is Mick Herron, after all), and we see a side of Sarah she’d previously kept hidden. “Inside, Sarah was storms and hurricanes. Twisters. Summer madness.” Herron’s incisive portraits, of everyone from Sarah’s awful husband, Mark, to her hippy friend, Wigwam, are as pitch perfect as ever, and even if you’ve read this series before, it’s worth reminding yourself of its excellence.

I am a huge fan of Janice Hallett, from The Appeal to The Mysterious Case of the Alperton Angels, so I was excited to get my hands on her latest, The Examiner (Viper), which has the excellent setting of an art course at the (fictional) Royal Hastings University. As ever with Hallett, it’s told in an innovative way: an external examiner is looking over the mature students’ coursework and comes to believe that one of them has been murdered. The reader reviews their various essays, emails and messages along with him, trying to work out a) if anyone is actually dead at all, and b) if so, who might have dunnit. The students are an intriguing crew, from City boy Cameron to the talented and ambitious young Jem (“Just this summer I took a course in sound electronics that meant I had to go to Stevenage every day for a week. That’s how committed I am”). The plot gets increasingly complex as they are asked to design an art installation for a local company, and mysterious radios get involved. I can’t fault Hallett’s ingenuity and her characters are a lot of fun, but this all became a little too convoluted for me by the end.

Britain’s favourite lexicographer Susie Dent has turned to crime, with the release of her debut novel, Guilty By Definition (Zaffre). Suitably enough, this follows the fortunes of a dictionary editor, Martha, who is back in Oxford after many years’ absence following the disappearance of her older sister, Charlie. When a cryptic letter comes to her workplace at the (fictional) Clarendon English Dictionary, hinting that secrets about Charlie’s disappearance have been covered up, she and her fellow lexicographers start investigating.

By dint of their (and their creator’s) occupation, there is an awful lot of etymology scattered around as they uncover the mystery at the novel’s heart. They’re always considering a word’s history, which, while fascinating, slows things down in a crime novel. All sorts of celebrities (from Shirley Ballas to Bill Clinton) are writing crime these days, with varying degrees of success. Dent’s love of words gives her a head start on most.

• To order Death at the Sign of the Rook, Down Cemetery Road, The Examiner or Guilty By Definition, click on the titles or go to guardianbookshop.com. Delivery charges may apply