The vast collection of wood engravings in this book comes mainly from chapbooks and toy books dating from the 18th and early 19th centuries. Some, are the work of Thomas Bewick (1753-1828), a renowned artist from the North-East of England ( http://en.wikipedia.org/wiki/Thomas_Bewick ) who at that time was at the peak of his career.
When this edition was produced in the fifties, Joan Hassall, R.E. (at the time considered to be one of the best wood engravers working in Britain) was brought in to create new work for the rhymes that had no existing illustrations. Her collaboration on this project lasted for two years but, unfortunately, she was not credited on the specific pieces she created so it is not possible for us to tell which is her artwork! For example, on the "Old Mother Hubbard" rhyme, below, there were three missing engravings which she had to re-create in order to complete all nine verses. Her engraving skills and talent were of such high standard that they look like they were made some two hundred years earlier! Here is the biography of Joan Hassall (1906-1988) on Wikipedia: