Struggling with this. The 1871 transcript has William Harrison, 48, Brother, as Married but the original reads very much like "Unm". So if this is his child she wouldn't necessarily be a Harrison! (Selina Jane's birth record per GRO 1861 Warrington district has the MMN Harrison, Selina a rare name so this probably right).
OTOH the birth record of Margaret Hughes 1904 Warrington has the MMN Howard -though there is another in the district 1903 MMN Thomas, which doesn't help! I'd expect she used the name Howard if that family brought her up. I note that there are 3 living children in 1911 - one possibly Ellen Agnes, the other one of William's and grown up? Searching Hughes-Howard births 1901-1915 not much help).
The baptism record has Howard in the wrong column and in heavier ink, so it may be a later addition (I don't think it's a different hand).
Sorry to be not much help but I'm trying to eliminate stuff. Sarah a daughter of William Harrison and some other Howard or Thomas misnamed on the 1871? (We rely on the enumerator). I fear the marriage may have not happened. If Sarah definitely a widow did William have a wife living? Bigamy a crime, co-habitation easily disguised, especially if you move.
Chris