Thanks Mo,
I get it now, you think she may have been born out of wedlock. Then she may be registered in the name of Sarah Mason

This is the family on the 1851 census...
1851 Census
7 Buckley Street, Manchester
James Smith - head mar 28 - Cabinet Maker - Yorks Halifax
Diena Smith - wife mar 32 - Yorks Halifax
Sarah Mason Smith - daur 7 - Yorks Halifax
Mary Ellen Smith - daur 5 - Yorks Halifax
Martha Smith - daur 3 - Yorks Halifax
Hannah Lassay Smith - daur 7mths - Lancashire
I think what I may do is send for her sisters birth certificate - Hannah Lassay Smith and then I will write to the registrar in Halifax about Sarah Mason Smith as I would really love her birth certificate with her being my GG Grandmother.
OK, thanks for listening and I appreciate your thoughts on the matter

Best wishes Vanda