How does this fit in with the ages of your Bagnall's? It's from the 1881 British Census:
Dwelling: No 6 Warstone Lane Census Place: Birmingham, Warwick, England Source: FHL Film 1341717PRO Ref RG11Piece 3003Folio 87Page 1 Marr Age Sex Birthplace Sarah BAGNALL M 41 F Birm'm, Warwick, England Rel: Head Occ: Pen Maker Elizabeth BAGNALL U 18 F Birm'm, Warwick, England Rel: Daur Occ: Pen Maker Thomas H. BAGNALL 16 M Birm'm, Warwick, England Rel: Son Occ: Jeweller Frederick BAGNALL 15 M Birm'm, Warwick, England Rel: Son Occ: Engraver Walter BAGNALL 12 M Birm'm, Warwick, England Rel: Son Occ: Scholar Sarah A. BAGNALL 10 F Birm'm, Warwick, England Rel: Daur Occ: Scholar
If the above is your group, then I also found this birth record:
Walter BAGNALL Sex:M Event(s): Christening:6 Jun 1869 Saint Stephen, Birmingham, Warwick, England Parents: Father:Thomas Henry BAGNALL Mother:Sarah
and then using the father's name, found:
Thomas Henry BAGNALL Sex:M Marriage(s): Spouse:Sarah PAYTON Marriage:29 Sep 1861 Saint George, Birmingham, Warwick, England
The above two are from www.familysearch.org . I also have the 1851 census for Warwick and took a look for Sarah Payton and Thomas Henry Bagnall and found:
Head: PAYTON, Joseph Neighbors268595 Name Relationship Mar Age Sex Occupation Birthplace JosephPAYTON Head M 64 M Carpenter Birmingham-War MaryPAYTON Wife M 54 F --- Solihull-War SarahPAYTON Daur U 30 F --- Bordoley-War Mary C.PAYTON Daur U 24 F --- Bordoley-War SarahPAYTON GDau - 11 F --- Birmm-War Address: 125 Well Street, Birmingham Census Place: Birmingham Birmingham, Warwickshire PRO Reference: HO/107/2058 Folio: 491 Page: 16 FHL Film: 0332120
Without Thomas' age, I could not determine his family.
I then went back to familysearch.org and found a birth record:
Sarah PAYTON Sex:F Event(s): Christening:25 Oct 1841 Saint Phillips, Birmingham, Warwick, England Parents: Father: Mother:Sarah PAYTON
So it seems she was illeg.
The above is not proof of anything, but all the names and ages line up and I hope something in here is helpfull in getting your search started.