Thank you all, some very useful links for me to read through. I'm wondering if the child was sent to live with a grandparent then would the grandparent be most likely to be supporting her? I suppose it all depends on circumstance.
I will try to share what I know, if you could tell me what you think...
My 3x ggm Catherine Johnston was born in Schoose, Workington, Cumberland in Jan 1855, I have her birth certificate which also tells me her mother was Ann Johnston, no father recorded.
Here she is in the 1861 Census living with her grandmother:
Name Cathrine Berwick
Age 6
Estimated Birth Year 1855
Relation Granddaughter
Father's Name James Johnson
Gender Female
Where born Workington
Civil parish Workington
Ecclesiastical parish St John
Town Workington
County/Island Cumberland
Country England
Registration district Cockermouth
Sub-registration district Workington
ED, institution, or vessel 20
Household schedule number 23
Piece 3939
Folio 101
Page number 6
Household Members
Name Age
Catherine Johnson
James Johnson
Cathrine Berwick
Mary Ann Johnson
Joseph To Todd
She is living in Schoose, Workington which was a tiny little village, her birth certificate tells me she was born there and my grandmother also told me she was from there before I began my research so this must be her. I think the spelling Berwick here is an error and should be Bewick. She gives her children the middle name Bewick, which is still passed down in the family today, and my grandma was told we were related to Thomas Bewick the famous engraver.
Catherine didn't live with her mum Ann at any point (as far as censuses show) but I think this must be Ann in the 1841 census living in Schoose:
Name Ann Johnstone
Age 10
Estimated Birth Year abt 1831
Gender Female
Where born Cumberland, England
Civil parish Workington
Hundred Allerdale above Derwent
County/Island Cumberland
Country England
Registration district Cockermouth
Sub-registration district Workington
Piece 159
Book 10
Folio 24
Page number 4
Household Members
Name Age
Thomas Johnstone 50
Catharine Johnstone 50
Henry Johnstone 15
Barnet Johnstone 14
Samuel Johnstone 12
Ann Johnstone 10
James Johnstone 7
An Ann Johnston born 1831, Workington married Martin Bewick in 1860, 5 years after Catherine was born and just before their daughter Jane Bewick was born. So my hunch would be that Martin Bewick was her dad as she uses the name Berwick when she is 6, but on everything else, birth, marriage, censuses etc she is Johnston.
Sorry for long post but if anybody has any thoughts on how I might find proof that Martin Bewick was Catherine's father that would be appreciated.