I would go for Rosemary Sutcliff's The Armourer's House illustrated by C Walter Hodges. He did a lot of very fine "everything in the text fits into the picture" work during the forties and fifties, and that book has a wonderful sailing-ship-being-built-at-Deptford picture which I absolutely loved as a child. I think he illustrated other books of hers, and some of his own, but that's the one that sticks in my memory.
Arthur Hughes is another very classic children's book illustrator; At the Back of the North Wind by George MacDonald might be his most well-known, and the book's a classic even if it is rather preachy by now-standards.
In addition to those already mentioned, I would like to recommend
Anne Yvonne Gilbert - Wild Swans, and Dracula which is one of my favourites. There is also a Folio Society version of The Vampyre if you are into Gothic literature. She also did the illustrations for the Game of Thrones colouring book a few years ago.
Christian Birmingham - He has done loads; The Snow Queen, The Little Mermaid, The Lion The Witch and the Wardrobe amongst many other classic literature.
I always think of Niroot Puttapipat as the modern equivalent of Rackham/Nielsen - his illustrations are stunning. Google the folio society Red Fairy book for an example.
Modern illustration i’ve loved - Angela Barrett (eg Snow Queen) Chris Riddell (eg The Sleeper and the Spindle), Inga Moore (esp Wind in the Willows), Alan Lee (Lord of the Rings), Brian Froud (see Faeries).
Golden age illustrators similar to the ones you like - Edmund Dulac (Perrault’s fairy tales), E.J Detmold (Arabian Nights), or either of the brothers Charles Robinson or W.Heath Robinson - both did lovely fairy story collections. If you like Nielsen, you must get “East of the Sun, West of the Moon”, it’s so so beautiful.
FWIW, the Everyman’s Library Childrens Classics are small hardbacks with many of the famous illustrators covered and are beautiful little books (when you can find them on sale, which is relatively often i’ve found, as their rrp is a bit steep).
The Magic Pudding is an Australian classic written and illustrated by Norman Lindsay. May Gibb's Snugglepot and Cuddlepie has the most beautiful illustrations. The original Blinky Bill written and illustrated by Dorothy Wall. Ida are toil Outhwaire's Elves and Fairies. All of these are available in lovely facsimile editions.
A personal favourite is The Fortunes of Poppy Treloar by Pixie O'Harris (who was a wonderful illustrator of all kinds of books), but I have no idea if there are modern reprints.
Thank you - Ardizzone is a great suggestion, and the Mayhew link is fabulous! Jan Pienkowski's illustrations are gorgeous and 'The Kingdom under the Sea' and 'A Necklace of Raindrops' were childhood favourites. Love Joan Aiken's books www.joanaiken.com/
I second the recommendation for James Mayhew on Twitter - he has reminded me of some beloved books from childhood and he inspired me only this week to pick up a second hand copy of Joan Aiken's 'Kingdom Under The Sea'. (I always loved Jan Pienkowski's cut paper illustrations.)
We have the Helen Oxenbury version of Alice in Wonderland...much better than the (weird and slightly scary) Tenniel line drawings. And Winnie the Pooh etc. with the original Shepard illustrations. We also have quite a few books illustrated by Edward Ardizzone, including the “Tim & Ginger” series, and “A Child’s Christmas in Wales”.
While she’s not exactly ‘classic’, at least not yet, Jackie Morris’s illustrations are just brilliant. We have her version of ‘How The Whale Became’.
Folio Society have some beautiful (if pricey) illustrated editions.
Any recommendations re beautifully illustrated classic children's books? Ideal presents for a family library? Have 'The Wind in the Willows' and 'Cinderella' illustrated by Arthur Rackham, and 'Fairytales of Hans Christian Andersen' illustrated by Kay Nielsen - any other suggestions?