In the most recent iteration of the TV show The Worst Witch, two of the teachers are Hecate Hardbroom and the headmistress, Miss Ada Cackle. I couldn't help but notice that their personalities seemed slightly similar to two characters from another famous series about a magical boarding school.
Hecate is tall, dark-haired, has dry and biting sense of humor, bullies the students verbally, and in the very first episode seems to betray the headmistress to side with a villain, only to be simply pretending in order to betray said villain.
Miss Cackle is somewhat elderly, with white hair (albeit seemingly dyed slightly blond), sharp light-colored eyes, and wears pince-nez spectacles. And of course she is a kind and powerful witch. She likes to give long rambling speeches before meals, and her favorite sweet is lemon drops.
On the other hand, the first books in the Worst Witch series came out in the 1970s, long before Harry Potter.
How much of these aspects of their characterization were already established in the books?