M E Buckingham (the pseudonym of Agnes Mary Easton) wrote several books about animals (Argh, the Tale of a Tiger is a particularly memorably named one). She wrote two pony books for the Country Life Library, both illustrated beautifully by K F Barker.
Finding the books
Usually reasonably easy to find. Zong can be very expensive with its dustjacket.
Links and sources
Many thanks to Amanda Dolby for the picture.