Andrew Higinbotham is a bit of a mystery at this point, as regards his origins. He never seems sure of his age on the census returns, and on his marriage certificate his age is given as that annoyingly vague "full" - therefore at the moment I can't be too sure of his date of birth. The likely deaths index entry in 1889 gives his age as 70, meaning he was born about 1819, and that's the best I can do. He says he was born in Ireland. On his marriage certificate he gives his father's name as Henry. His father's occupation was what looks like "Land? steward" - definitely a "something" steward, anyway.
(I have found a Henry Higinbotham on the census, who may be Andrew's father - a Landed proprietor, born about 1784 in Dublin, in 1851 living with his daughter Rosanna in Plymouth. But nothing to confirm the connection.)
Andrew, a bookbinder at the time of his marriage to Elizabeth Longbottom, continued in this trade throughout his working life, first in Derby, later in Leeds. The move to Leeds may reflect changes in the local printing business in Derby, and specifically in the firm of Richardson and Son - evidence points to Andrew working for this company, though as yet I've no confirmation.
The IGI shows that Andrew Higinbotham, son of Henry Higinbotham, married Elizabeth Longbottom, daughter of Thomas Longbottom, at St Werburgh, Derby, on 19 June 1859. As both Andrew and Thomas were bookbinders by trade, this is presumably how Andrew and Elizabeth met. The marriage was by certificate - rather than by banns.
At the time of their son William's birth, seven months or so after the marriage, the family were living at 119 Friargate, Derby. This was, at the time, the home of Elizabeth's grandfather, William Pegg. (Presumably William Higinbotham was named after his great-grandfather.)
A year or so later, by the time of the 1861 census return, Andrew and Elizabeth and son William have moved to Merchant St, in Derby, a side-street not far away from their previous address. In 1871 they're still in Merchant St, at a different house (or the same house, renumbered?). Andrew and Elizabeth now have three more children, Ann, Andrew and Thomas.
Andrew is still working as a bookbinder.
Perhaps because of changes in the local printing industry, they've moved by the time of the 1881 census, and are living on Reuben Street, in Leeds, West Yorkshire. Andrew says he is aged 63 - though he seems to have aged by 12 years between each census, rather than 10.
The deaths index shows that Andrew Higinbotham died in 1889, in Leeds, aged 70.