"She was the first mystery writer I read," she says. "I discovered her when I was about 12 and I'd read all her books by the time I was 14. The thing about Agatha's books is that they never simply started off with, 'Here's a dead body. Who killed him?'
"There was always some element of the apparently impossible before Agatha goes on to show how it was actually possible. I've always been very attracted to that and always had that in mind when I've written my own books."
Beginning with a trio of vicious murders at the glamorous Bloxham Hotel in central London, Hannah originally came up with the central premise for The Monogram Murders long before she was approached to write the novel.
"The first idea I had was for the ending, which I regarded as a very ingenious, high-concept solution to a mystery. I tried to use it in one of my contemporary thrillers and it just didn't seem to belong in any of them, so I shelved it and decided to use it at some point in the future. Then when the prospect of writing this book eventuated I thought to myself that this idea would be perfect for Poirot, and then everything else fell into place."
Set in 1929, The Monogram Murders occurs in the gap between 1928's The Mystery Of The Blue Train and 1932's Peril At End House. "We didn't want to bring Poirot back from the dead, because Agatha killed him off in her last book," says Hannah. "We also didn't want to do a prequel because everyone knows The Mysterious Affair At Styles is the first Poirot. It would have felt disrespectful to mess with any of that, so what I did was slot my book in the four-year gap when Christie didn't write any Poirot novels.
"It was a time when she was a bit fed up with Poirot, so she wrote the first Miss Marple novel as well as a few plays and a standalone novel. Poirot is unaccounted for during that period, so I decided to set my book then."
A variation of the classic locked-room trope, Hannah keeps the reader guessing until the very end. "There are in fact three locked rooms as there are three murder victims and each of them is found in a different locked room," she says. "But constructing the plot wasn't all that difficult. It all seemed to arrive in my head just when I needed it to, which was great. My subconscious must have been working overtime and I'd re-read all the Poirot books in preparation for writing, so it wasn't that hard at all."
Crucially, Hannah also created her own protagonist, in the form of feckless Scotland Yard detective Edward Catchpool.
"He's just an ordinary person the reader can identify with as he and the reader together are in awe of Poirot, who is just a brilliant mind," she says.
She was anxious not to mimic Christie's distinctive prose. "I wanted to invent my own narrator, a character who isn't in any of Agatha's books. By having him as someone who is working with Poirot, that seemed like a quite authentic and sensible way
to write about Poirot in a way that would be in a slightly different style to Christie because he is a new character."
But while Christie's words provided her main guide, Hannah was also inspired by David Suchet's memorable portrayal of the quick-witted sleuth in the ITV adaptations of the novels. "In my mind, Poirot looks like David Suchet," she says. "It was so brilliant that actually now Christie's Poirot and Suchet's Poirot are kind of one and the same. Certainly that is what I had in mind when I was writing the book."
While she is optimistic that The Monogram Murders will eventually reach the small screen, Hannah is unsure whether Suchet could be persuaded to return. "He has announced that he has finished playing Poirot. But on the other hand, he said that before he knew there was going to be a new book, so we may be able to tempt him back."
The Monogram Murders (HarperCollins $32.99) is out now.