If the name of the artist is not indicated, copyright probably expired at the end of 1984. (Where the creator of a published work is unknown, copyright expires 70 years after the end of the year in which the work was first published).
If the artist's name appears in the book, you'll have to Google their name to check that they died prior to the end of 1936. (Copyright lasts for 70 years from the end of the year in which the creator of the work died).
The only exception might be if the book was to be deemed a 'composite work' created by, say, a separate author and artist. In which case (assuming that their names are known), copyright lasts until 70 years after the end of the year in which the last surviving creator of the work dies. (So, it's possible that the artist might have died prior to the end of 1936 but copyright , in the book as a whole, might still exist if the author died in a later year).
http://www.copyrightservice.co.uk/copyright/p0 1_uk_copyright_law
Chris