I think you're going to have trouble as it definitely looks like an illegitimate birth.
Harriet LEAH seems to still be unmarried and living alone in 1881 census:-
Harriet LEAH Head Female 54 Bramhall, Cheshire Silk Weaver
Dwelling Benja Fold
Census Place Bramhall, Cheshire, England
Public Records Office Reference RG11
Piece / Folio 3486 / 95
Page Number 4
You should try the Cheshire Board for this query - you might have more luck
