I agree that William Greaves Hurd was the Son of Sarah Hurd.
I think she was Widowed though.
BENJAMIN Hurd Married Sarah CARPMEAL, 18 November 1812, All Saints, Derby, Derbyshire
(FreeREG)
Benjamim HURD, Servant, age 29 (birth c 1790) was Buried same Church, 28 Feb 1819.
(Familysearch.Org and FreeREG)
Trish

PS Welcome to Rootschat!