Do you have Henry's marriage certificate? If so who were the witness? they may just give a clue to his mother.
Norwell St. Laurence PR:
No.: 48
Date: March 9th 1846
Names: Henry Fricknell & Sarah Wilson
Ages: Of full age & Of full age
Condition: Bachelor & Spinster
Profession: Tailor & Dressmaker
Residence: Norwell & Norwell
Fathers' Names: --- & Thomas Wilson
Fathers' Professions: --- & Farmer
Witnesses: Elizabeth Wilson, Barnabas Williamson
I've no clue who Barnabas Williamson was, but I think that Elizabeth Wilson was Sarah's mother.
Another thought On 1841 neither Frances or her sister Sarah are shown as working, so presumably their father was earning enough to keep them.
Have you followed Sarah through later years?
Also who were the parents of Mary who was living with them?
Mary was the illegitimate daughter of Sarah. Sarah also had another daughter Ann who was born in 1827 and died in 1828. Later on Sarah married William Shipley in 1853 at Nottingham St. Mary. She died in 1868.
Who were the parents of the 3 Frecknell boys living in Worksop with Isaac and Lyddia Radford in 1851, the youngest one says born Southwell c1844?
HO107; Piece: 2122; Folio: 154; Page: 15;
These three children were the sons of William Merrills Frecknall and Elizabeth Nelson. They were of a branch of Frecknalls that came from the North Leverton/Retford/Worksop areas. They are distantly related to Frances - though I haven't been able to work out the exact relationship. It may be a coincidence that they both ended up in Southwell.