Before going on to the marriage it would be wise to be clearer about William's birth.
William Henry Walker born 24 June 1851 was baptised at St John the Baptist, Halifax, 31 Aug 1851; parents Thomas (overlooker) and Charlotte, of Skircoat.
His birth was registered at Halifax, Sep qtr 1851, mother's maiden name VINT.
(Thomas Walker married Charlotte Vint at Halifax, Dec qtr 1841).
What is your source for the Thomas Beresford Walker/Charlotte Buergin family - can you point us to them?