In 1841, William (12) was with his mother Jane and siblings.
In 1851, William Mather (24) was a boarder of Henry and Mary Shaw and a shoemaker at 62 Leeds Street, Liverpool. There was an insert showng brother-in-law which is unlikely (unless from an earlier marriage). There were also William (22) and Ann (20), children of Ralph (48 ?) at Baugley Lane, Audenshaw
In 1871, William Mather (44) was a shoemaker at Dale Street, Liverpol boarding (and probably working for) James Blundell, a master shoe maker.
In 1891, William Mather (63, born Droylsden) and Edward Blundell were lodgers at Mescar Lane, Downholland, Ormskirk. Both men were single, and shoe makers.