"With The Monogram Murders, I loved the central idea but it wasn't absolutely simple," she admits. "It had a kind of multi-layered revelation, so it was more labyrinthine and harder to write. With Closed Casket, I just needed to place the suspects in the setting, and then a certain person would turn out to have committed the murder for a particular reason, so it was more straight-forward."
With Inspector Edward Catchpool returning after making his debut in The Monogram Murders, Closed Casket features several allusions to the earlier novel, although Hannah is quick to stress that the two books can be read in either order.
"I tried to keep mentions of The Monogram Murders to a minimum because it's really important that each of them stands alone, but it's included to mainly to show something about Joseph Scotcher's character," she says, referring to Lady Playford's terminally ill secretary, in whose favour she changes her will in Closed Casket's first chapter despite him only having mere months to live.
"Scotcher is the sort of person who will make you feel good about yourself, and that's why Lady Playford adores him," continues Hannah. "Catchpool is feeling bad because when he first worked with Poirot, people wrote horrible things about him in the newspapers, saying that he was useless and that Poirot was a great genius.
"Until he meets Joseph Scotcher, nobody had taken the trouble to make Catchpool feel good about himself by pointing out that 'just because you're not Poirot, doesn't mean you didn't do a fantastic job as well.'"
Having opted not to tell her two Hercule Poirot novels to date from the perspective of the Belgian sleuth's usual partner-in-crime-solving Inspector Hastings, Catchpool has provided Hannah with her own distinctive viewpoint into the world that Christie created.
"I thought that coming up a new sidekick for Poirot, who could also be the narrator, would be a very sensible way to get around the fact that my Poirot novels would have a slightly different tone and style than Agatha's," says Hannah, who also wanted Catchpool's professional performance to gradually improve during the course of the two books.
"In The Monogram Murders, he's riddled with anxieties and self-doubt, and is constantly over-thinking and worrying," she continues. "He did have the odd flash of brilliance but was a bit slow on certain occasions. Then in Closed Casket, he is a bit better as a detective - having already worked with Poirot once - so he's much more confident, although nowhere near as much of a genius as Poirot."
Hannah insists that Lady Playford is not actually modelled on Agatha Christie herself.
"As a character, she is not at all like Agatha, who was very nice and quiet, and was very interested in other people," she says. "She wasn't a bit like Lady Playford, who is manipulative and attention seeking. But I did want her to be a mystery writer, and her fictional character, Shrimp Seddon, is meant to be a bit like The Secret Seven or The Famous Five."
Indeed Lady Playford actually has more in common with Hannah herself.
"She's kind of like a really mischievous version of me, who is always trying to do really strange, weird things. Changing her will in the first chapter for some bizarre reason is very much like me, but of course it doesn't work, as it goes disastrously wrong."
Maybe Hannah wishes she was more like Christie as an author, having written "detailed plans for the whole novel with every event in the order that they were going to happen", for both The Monogram Murders and Closed Casket. It's a process that has never proved to smooth for her own novels, such as psychological thriller The Narrow Bed, which was released earlier this year.
"If I try and do that with my own novels, it never quite works out quite so neatly," Hannah says. "My mind just works in a neater and clearer way when I'm writing Poirot because Agatha's mind was so neat and clear.
"Her books were crystal clear at every stage, as you're mystified and you don't know the solution to the mystery, but everything that you're supposed to know is so clearly and crisply laid out, so writing continuation novels for her has made me think in a clearer, crisper way."
Revealing that she wouldn't rule out doing it long term, because she has one detailed idea for a novel and a couple of other settings she'd like to try putting Poirot in, Hannah is open to the prospect of writing a third Hercule Poirot opus.
However, she wouldn't be interested in taking on Agatha Christie's other well-known protagonist, Miss Marple.
"I couldn't do Miss Marple because I've already done Poirot, and so it would just feel like I was really trying to be Agatha," she says. "Poirot is more than enough for me, but I would love it if someone proper, who really loves Miss Marple and could do it well, was to write new Miss Marple mysteries."
Closed Casket: The Brand New Hercule Poirot Mystery
by Sophie Hannah
HarperCollins, $35