Delwyn,
Here is a long shot for you. I have no idea if this record is from the right area. The info is from an 1851 census (citation at the bottom.) The daughter, Caroline is approx. the right age to have been born in 1833, and the mother and father have names that might fit.
https://www.familysearch.org/ark:/61903/1:1:SG52-N9S
Richard Oliver Head M 49 Wapping,
Mary Oliver Wife F 45 Wapping,
Mary Ann Oliver Daughter F 19 Wapping,
Caroline Oliver Daughter F 17 Wapping,
Sarah Oliver Daughter F 14 Wapping,
Isabella Oliver Daughter F 9 Limehouse,
Richard Oliver Son M 8 St Georges East,
Joseph Oliver Son M 1 Whitechapel,
"England and Wales Census, 1851," database with images, FamilySearch(
https://familysearch.org/ark:/61903/1:1:SG52-N9S : 21 October 2017), Richard Oliver, Saint Mary Whitechapel, Middlesex, England; citing Saint Mary Whitechapel, Middlesex, England, p. 21, from "1851 England, Scotland and Wales census," database and images, findmypast (
http://www.findmypast.com : n.d.); citing PRO HO 107, The National Archives of the UK, Kew, Surrey.
Do you have any good way of deciding whether or not this could be the family you are looking for?
Reba