No one besides J.R.R. Tolkien illustrated the first British edition of The Hobbit. Tolkien supplied the book’s illustrations, including its maps and drawings, for the George Allen & Unwin edition published in 1937.
The original volume included visual material that helped establish the appearance of Middle-earth, such as the map of Wilderland and the map of the Shire. Tolkien’s artistic work was part of the book’s design rather than an afterthought.
This fact is sometimes confused with later Tolkien editions and other fantasy books, which often feature professional cover artists or illustrators. Pauline Baynes illustrated several Tolkien-related works, including Farmer Giles of Ham and The Adventures of Tom Bombadil, but she did not illustrate the first British edition of The Hobbit.