A very kind correspondent by the name of Yukiko has told me about an upcoming Studio Ghibli production of The Borrowers.
There is more information at the Ghibli blog, but it is to be called 'Karigurashi No Arrietty' (Arrietty the Borrower) and will be directed by Hiromasa Yonebayashi. Instead of being set in 1950s-era England it will be set in the present-day Tokyo neighborhood of Koganei.
We have been watching the BBC adaptations from the early 1990s - so much better than that American version - and are now looking forward to seeing the Ghibli version. I also need to buy a new copy of the Mary Norton novels as it is years (and years) since I've read them. Recently I read Bed-Knob and Broomsticks for the first time and it was so much better than I was expecting after having seen the Disneyfied version as a child. I wouldn't mind seeing a Studio Ghibli version of that one too.