John and Honor Wareham's children, according to the IGI and the 1841/51/61 censuses were Eliza (1837), Emma (1838), Elizabeth (1841), Francis, Charlotte, Margaret and Susan.
The only son is living as a 17 year-old servant in 1861, so it seems likely that Eliza Jane was the illegitimate daughter of one of the first three girls. Emma (12) and Elizabeth (10) were both living at home in 1851 and Honor was on parish relief.
Under those circumstances it was not uncommon for the grandparents to bring up the child.
Richard