It might be that he was know as John William after his father. Have you looked at this 1901 census entry from Frimley, Surrey...
John W Parker abt 1862 Frimley, Surrey, England Head, Coachman
Fanny Parker abt 1854 Fremington, Devon, England Wife
Francis T Parker abt 1888 Frimley, Surrey, England Son, Under-gardener
John W Parker abt 1885 Hampstead, Middlesex, England Son, Under-gardener
Hilda C Parker abt 1890 Frimley, Surrey, England Daughter
The occupations are interesting.
Could the names of the witnesses at his marriage help?
Best regards,
John