Jessie bond left for London in 1878 so William would have chased her there after that point. He might still have been a widower when the 1881 census came out.
I did a random search of the 81 census, inputting First Name William, born Liverpool, Lancashire, 1843-53 (so up to ten years older than Jessie), search terms widow or widower, male. Then I eliminated those who didn't have a couple of kids and wasn't 'prosperous'.
These are the individuals I came up with.
William Cairns, 1852, 8 Lundie St., Miller (Arty), children William 7, Frances 5
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William Drew, 1848, 119 Richmond Row, Draper, children William J. 8, Jas. B. 4
William Hughes, 1848, 54 Chester Rd., Master Builder (Out of Business), Lilian 4, Florence 3
William A. Kelly, 1844, Demesne St., Poulton Cum Seacombe, Grocer (employing 2 men), .........................Amy E 8, William R 7, Percy C 5, Ernest A
William Singleton, 1845, 17 Guest St., Shipwright, Thomas 14, William 9
The one with four kids is the one I had in mind so I squeezed him in. His childhood home (1861) was on Bostock St., Liverpool, only 1 1/2 kilometers from Norton St. where Jessie lived.
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