The only other Walter WILLIAMS born Wallasey I can see on the 1901 census is a widower aged 36, with children Francis (10) and Gertrude (3), but that would put his date of birth around 1864....

Do you have a definite date/place of birth for any of "your" Walter's children? If not, it would be helpful to get a copy of his marriage cert if/when funds permit to confirm his age and father's name.
If Jane Ann's first married name was SALKELD, she was born in Cumberland c1873 (according to the 1901 census), and apparently married Walter in the first quarter of 1911. The free index of the 1911 census shows a Jane Ann WILLIAMS born Cumberland c1873 living in Birkenhead, so maybe worth investing in a few credits?
Added: on Free BMD there's a death for William WALTERS in Wallasey district in 1937 aged 72 - that would match the guy above.Rambler