Many in the UK of all ages would admit that they were or are fans of Enid Blyton. In fact, her books have just been re-printed in an illustrated form and very slightly up-dated.
I'm sure that children's UK authors, apart from such writers as J.K. Rowling, Michael Morpurgo and Jacqueline Wilson, would wish for such popularity. However, there was one time in the 20th century when her books were banned from some libraries and many schools on the grounds that her stories were repetitive and her choice of language was simplistic. However, like the Harry Potter series, she made readers from children who would never have picked up a book otherwise.
Apart from the many objections to her books from the educational establishment, it is interesting for any author to try to understand her lasting popularity. Several books have been written on this subject, but from my recent reading of her work I'd say that one reason is because the adults don't interfere with the children's lives. They are missing from the stories. The children always outwit stupid adults, they have adventures which the readers would long to experience. Food is an important subject. There are always animals with whom to share their adventures. There is conversation between the children themselves without adult intervention and a great deal of it on each page with very little description to slow things down. The relationships between the children are believable, and most importantly, the children always succeed in whatever they do and there is always a happy ending. And perhaps, more importantly, something happens on every page.
It would be interesting to contrast these books with the equally popular ones today, such as Dustbin Baby written by Jacqueline Wilson. She writes about dysfunctional families and has despairing endings.... but that's another story.