As you can see there are discrepancies about her age at emigration, but the passenger list clearly shows her as 7 years old. She is in a list of children of various surnames and of various ages but the youngest were 6 years old, not 2 (2 seems extremely young to be shipped abroad?). Maria Rye sailed from Liverpool so it might be that Liverpool/Manchester were considered the child's place of birth as it's the last city she could remember. Maria Rye seems to have scooped up children from London in particular, taking children brought to her by relatives as well as the ones she took from homes. However according to
https://www.bac-lac.gc.ca/eng/discover/immigration/immigration-records/home-children-1869-1930/home-children-guide/Pages/maria-rye.aspx#d she did take children from Kirkdale Industrial School, and Liverpool/Salford workhouses too and Salford adjoins Manchester.
Myself and cousin's common ancesters are Eliza Cox (b.1835 Northampton - d.1886 Wellingborough) and Charles Holmes (1830 Northampton – 1912 Wellingborough) married in 1855 in Raunds. Eliza was the oldest of 8 children of Thomas Cox and Frances Bull. Charles was one of 10 children all born in Northants of John Holmes (born Lancashire) and Sarah Brown (born Northants). We think our weaker genetic connection with X could be a generation earlier. There's nothing obvious on Eliza Cox's side of the family, who are mostly Northants based, but if Millicent was from Manchester, then a male relative of John Holmes, born in Broughton, Lancashire abt 1786 (according to the 1851 census), might be a candidate as her father, or one of his female relatives as her mother? John Holmes died in Northants in 1861.
We have looked up many spellings of Millie/Milli/Millicent plus or minus Alice, and Cocks and other similar sounding surnames, along with births of females in that month and the year range, but any found can be traced as later living/marrying in England so are not X’s grandmother. Neither have we arrived at many possibles regarding year and geography that could link with someone in our family. I have wondered whether there was a family connection between Millicent Alice and her new adoptive family – was her adoptive family (Bellamy and Parsons) related to her biological parents?
Whether the surname is a red herring in this case is anyone’s guess! Did Millicent Alice Cox take her surname from her mother or her father? Were her parents married or cohabiting and her father then died or the parents separated? Her mother was described as in poor health. Did she die soon after or recover, or was this a fabricated reason for removing the child? Was the child illegitimate or another excuse to take her away. Did she invent the name for a father when she married, giving her husband’s name in a panic?
John Holmes family in Broughton, Lancs and their whereabouts might give us some clues?