The first thing is to lay out all the information you have:
1857: what was the occupation of William and his father William, the age of William, his address, the witness names?
What censuses do you have the family on?
If you don't have any census records for them, when and where were their children born?
Did this family stay in the UK or emigrate?
http://www.rootschat.com/forum/index.php/topic,225609.0.htmlThere is someone here related to the same family. I see from here that Mary is b. 1837 Carlton.
From this I can see them in the censuses:
1881: William aged 53, b. Bisdale
1871: William aged 43, b. Bisdale
1861: William aged 33, b. Bisdale
(pretty obviously them as they have a son called Hindson).
www.familysearch.org shows a quite likely record in Bilsdale Midcable in 1828 for William son of William Garbut and Elizabeth; in 1841 this family are in the census and William senior, like your William in later censuses, is a stonemason. However the surname seems reasonably common in the area so it's worth being a wee bit cautious as you move back.