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Alma,
If you take another look at the baptism for Samuel John Hall, it is noted that his mother was:-
Mother's name: Hannah Sulivan Hall
....could very well be that her maiden name was Sulivan/Sullivan.

1891 wife is noted as Annie born Pimlico, and
1901 wife is noted as Annie Hall born: Ireland

Hannah and Annie could of course be the same person but to be absolutely sure who is the mother of Samuel, as Mike has already said, you would have to buy his birth cert. and you would also have to buy the cert. for his brother Edward to see if they have the same mother.

Here's something interesting:-

1881 shows that the father of Samuel (1865) is Edwin. Keeping in mind the name Sullivan from the Baptism of Samuel (1889) I'm wondering if this could be a marriage for Samuel Jnr.

Name: Samuel Hall
Age: 29
Estimated birth year: abt 1865
Occupation: Traveller
Address: 27 Waterfront Road
Spouse Name: Norah Sullivan
Spouse Age: 27
Fathers Name: James Sullivan
Occupation: Builder
Record Type: Marriage
Marriage Date: 27 Aug 1894
Parish: St James, Fulham
County: London
Borough: Hammersmith and Fulham
Father Name: Edwin Hall
Occupation: Brass Finisher

Father's name and occupation fits with census.
Also Samuel's occupation fits with 1901 census.
Parish of Fulham also fits.

Could also be just a big coincidence.

only other marriage in Cheshire
Name: Samuel Hall
Spouse Lilian Ellison
Date of Registration: Oct-Nov-Dec 1964
Registration district: Runcorn
Registration county (inferred): Cheshire
Volume Number: 10a
Page Number: 1002