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Curiously I can find a James Webb in correct quarter in Steyning mmn Shufflebotham. Can't find a likely marriage to fit in that area though.

could one of the son's be the father and died before 1921 and so did his wife? and grandma took care of Jimmie.

Or one of the daughters had a relationship with a Mr Shufflebotham and switched the surnames round when the birth was registered

A census record is only as good as the informant (Head of Household) knows. In 1921 (as in 1911) we are seeing the form the householder actually filled in, so we don't have the problem of any enumerator transcription errors. Of course, Alice snr might have though he was born in Hove but not asked the child's mother. When Jimmie was born, Hove would have been in the Steyning registration district.
Jimmie could have been a nickname, short for James, or his middle name could have been James, or his real name could be something unrelated to either Jimmie or James. (My OH says his father called him Charley when he was a child - he has three forenames, none remotely like Charles or Charley !)

I haven't found a likely earlier marriage for William in Ware (where he was in 1871) but there's 10 years before his next sighting in Tonbridge, and a lot of miles in between.

There's an Albert Cross (no middle name included) age 17 travelling from Liverpool to New York in 1918 on ship named Baltic

is this any help?

http://www.historywebsite.co.uk/articles/Darlaston/Education.htm