Both sets of figures show how authors such as Dahl, Blume, Blyton, Rowling and Rene Goscinny, who, with illustrator Albert Uderzo created the Asterix series, once dominated the charts.
Blyton, responsible for about 800 books including the Famous Five series, was the most borrowed author for the first three years covered by the survey, before entering a gradual decline and finally falling out of the top 10 in 2008/09.
Dahl, responsible for about has also lost his once eminent position in the charts over the same period, although he remains in the top 10, as the ninth most borrowed author, in 2011/12, the most recent year for which figures are available.
Blume, who wrote novels for girls, and Goscinny fell out of the lists in 1989/90 and 1997/98, respectively.
Rowling, who published her first Harry Potter novel in 1997 and wrote only seven books in the series, never reached the "most borrowed authors" list, but her works did dominate the charts for the "most borrowed children's books", taking the top five places in 2000/01 and 2001/02.
Since then, though, her presence in that chart has declined, and she dropped out entirely last year.
The study was conducted by Public Lending Right, part of the British Library, which monitors data from libraries and collects payments for authors.
It also shows how other children's series have emerged, bringing periods of dominance for their authors.
Among them are Jacqueline Wilson (Tracy Beaker), Francesca Simon (Horrid Henry), Daisy Meadows (Rainbow Magic), Lauren Child (Charlie and Lola) and Stephanie Meyer (Twilight). Julia Donaldson, responsible for The Gruffalo, Room on the Broom and Stick Man, has also dominated in recent years.
But some old favourites have endured. Where the Wild Things Are, published in 1963, was one of the most borrowed books in the 1980s, before disappearing from the lists.
However, it returned in 2010/2011 - before the death of author Maurice Sendak in 2012 - and remained in the top 10 last year.
We're Going on a Bear Hunt, by Michael Rosen, published in 1989, entered the top 10 in the same year.
Mick Inkpen, responsible for Kipper the Dog and Wibbly Pig, has appeared in every top 10 authors list since 1997/1998, and Allan and Janet Ahlberg, whose books date back to the 1970s and include Burglar Bill, Woof! and the Jolly Postmen, have also fared well. They were in every author list from 1989/90 to 2008/9.
PLR head Jim Parker said: "I remember when Blyton, Bloom and Dahl were the big names. But things change and fashions change. Parents have a lot to do with this and there is a different generation of parents now.
"Some of the works that have endured are those that seem timeless. There are books which could have been written in the 1970s or yesterday and you cannot tell. You can't say that for all the books."
Most borrowed
Going up:
* Jacqueline Wilson (Tracy Beaker)
* Stephanie Meyer (Twilight)
* Julia Donaldson (The Gruffalo)
Going down:
* Roald Dahl (Charlie and the Chocolate Factory, The BFG)
* Enid Blyton (The Famous Five)
* J.K. Rowling (Harry Potter)
Enduring classics:
* Maurice Sendak (Where the Wild Things Are)
* Michael Rosen (We're Going on a Bear Hunt)
Source: Analysis of lending at British libraries.
