Wikipedia has some details of Tom Hood (1835-1874).
The copy shown below is in the British Library at shelf mark 12808bb29. A full description of the cover design will be in the British Library database of bookbindings.
Tom Hood also illustrated this work, also written by his sister, Frances Broderip.
Broderip, Frances Freeling. My Grandmother's budget of stories and songs. With illustrations by her brother, Thomas Hood. London: Griffith and Farran, successors to Newbery and Harris, Corner of St. Paul's Churchyard, 1863.