Here is what I found out about Eliza Poole and Charles William Henry Cater.
Eliza Poole is Elizabeth Poole who I believe is actually Elizabeth Hiscocks the mother of Henry Charles and Stephen James . She was 56 in the 1841 census which would have put her birth at about 1785. I found a marriage record for Elizabeth Hiscocks to a William Poole in 1828 and Elizabeth was listed as a widow. What also lead me to believe this was Elizabeth Hiscocks is that she is in the same residence as Stephan (her son) and the women listed under Elizabeth are her daughters and Henry Charles and Stephens sisters. Martha Cater is Martha Hiscocks and she married a Charles Cater and they had Charles William Henry Cater. The Mary is also a sister. She is Mary Ann Hiscocks who later married William Rickards.
It appears Martha Cater died sometime after the 1841 census and this is why Charles William Henry Cater is living with Eliza Fulcher in 1851. I believe Eliza was not married and took him in to raise him, she would have been an aunt by marriage. Martha Cater (Hiscocks) had actually been married once before to a Edwin Trotman and they had a daughter Emma. Emma is actually the witness at Mary Ann Hiscocks wedding and she is visiting Henry Charles and Mary in the 1851 census.
Probably more than you were looking for but I wanted to share what I found.