Hannah Frances SHAW Salford

[jennifer c]

William Baggley born 23/11/1868

Jennifer

[Radcliff]

1871 census,St George district Manchester
Thomas Baggley aged 28 years,B Labourer born Manchester
Mary,wife aged 28 born Manchester
William aged 2 born Manchester
Mary J aged 4 born Manchester
Sarah E aged 5 months

[Ladyhawk]

Are you sure that Hannah's surname is Shaw? because there is a marriage 1889 Salford of a William Baggley to a Hannah Frances Stockar or Stockas

14.6.1889 at Paddington, Lanacashire William Baggley aged 21 father Thomas to
Hannah Frances Stockar aged 18 father William

Checking the GRO Index for Esther/Hester mmn is down as Stocker

BAGGULEY, WILLIAM    mmn BURNS    
1869  M Quarter in MANCHESTER  Volume 08D  Page 264

If this is same Hannah from marriage there is no mother’s maiden name on birth entry on GRO indexes this would suggest illegitimate

STOCKER, HANNAH  FRANCES   - (blank)
1871  D Quarter in MANCHESTER  Volume 08D  Page 23      

Haven’t found her on census

Edited

Have checked again and have had no luck with the 1881 census 

If you want to obtain her birth certificate an online pdf version costing £6 can be ordered from the GRO.
You will need to provide the full GRO index reference number for the record that you are interested in. It's free to register https://www.gro.gov.uk/gro/content/certificates/login.asp

Noticed whilst editing I'd inadvertently removed some info. re: William 

1871c RG10; Piece: 4053; Folio: 26; Page: 5
Thomas Baggley 28
Mary Baggley   28
William Baggley   2 manchester
Mary J Baggley   4
Sarah E Baggley 5 months

13 Dec 1863
Thomas Baggley 22 , cart sheet maker, 26 Back water Street
Mary Burns 22,
his father William occ Carver
Her father John shoemaker

William Baggley   30 wood carver
Mary Baggley   25
Thomas Baggley 9
William Baggley   6
Elizebeth Baggley 1
1851c  HO107; Piece: 2227; Folio: 612; Page: 19

BAGULEY, THOMAS  mmn    OLDMAN     
1842  J Quarter in MANCHESTER  Volume 20  Page 611   Order

19 Jul 1841 Manchester, St Mary,
William Baguley f/a, 34 Bottle St occ carver
Mary Oldman f/a 27 Deans Gate
his father Thomas mould maker
her father Francis brickmaker

[Radcliff]

possible
1881 census
Alerton Street Habergham Eaves
Thomas Duerden aged 49 a beamer
Mary Duerden aged 39
Sarah Stoker daughter aged 15
Hannah Stoker daughter aged 11
Elizabeth Duerden aged 12
Lucy Duerden AGED 8
Clara Duerden aged 6
Isabella Duerden aged 4 months
all born Burnley

[Radcliff]

Isabella Duerden birth reg Burnley 1880 mother Stoker

[Radcliff]

Holy Trinity Habergham Eaves
26th December 1885
Frederick Tungate Hooper aged 25,coach maker,bachelor of Catlow St
Sarah Stoker,aged 20 ,weaver,spinster of Elmwood st
Grooms father Frederick John Hooper Grocer
Brides father William Stoker,carvr and gilder
witness Henry Hooper and Isabella Duckworth

[Radcliff]

Possibly not the Hannah you are looking for she s with her parents William and Mary,in 1871