Wife Clara (born Woolwich circa 1870) is listed in Blackwell Road, Huthwaite in the 1901 census, with 3 children: Annie M aged 9, born Woolwich. Albert E aged 5 born Aldershot, and Walter C aged 11 months born Plumstead.
Only one of these children (Annie) is listed in Walter's Army Service Corps file.
In the 1911 census Walter junior, born Plumstead, is aged 11 and recorded as the son of Mary Hannah Buxton from Chesterfield. I wonder if this is the "Annie" referred to in CWGC. (There's a possible marriage in Chesterfield in 1901 - Walter Buxton and Mary Ann Tolley on same page)
And what happened to Clara?.
And why can't we find a birth registration for Albert Edward in Farnham/Aldershot?