I normally have to read a series in order because it goes completely against my nature to skip around. After reading Book 1 though, I was on the fence on whether or not to continue the series because, even though I enjoyed the mystery itself, the dialogue and British narrative was quite choppy and all over the place so I had a hard time following a long in certain parts.
I owe Themis-Athena's Garden of Books a huge thank you for recommending that I skip ahead to Book 6, Artists in Crime. I followed Themis's advice and I'm really glad I did because I enjoyed this story immensely. The writing is so much more polished in this book. The British narrative is more refined and easier to follow, the plot was well-developed and the mystery was complex enough that I didn't guess the murderer until it was pretty much handed to me on a silver platter. Overall you can just tell that the author's skill has evolved since her debut.
There are a whopping 32 books in this series so I can't say if I will go back and read books 2-5 anytime I soon but I definitely plan to continue reading the series from book 7.