I did find a William Harrison in 1861, 1871, 1881 censuses. He was born in England about 1808.
Do you think your William could have remarried? This William was married to a Hannah. Their first child wasn't born until 1856, so this william would have been 48 yrs. They lived in Trafalgar, Halton county, Ontario. In 1881 children were listed as: Sharlotte 25, Daniel 22, Louise 19, William 19, Harriet 11.
I wasn't able to find a marriage registration (Hannah was from Ontario)
Anyway, something to think about?