Marmaduke
Thanks for this, and thanks for all your help with this thread so far - very much appreciated!
I'm pretty sure this is the correct individual, although I had spotted the "Fixby" birthplace in the 1861 census and it did seem a bit odd at first. His 1851 census record gives his birthplace as "Halifax"; and his baptism record gives it as "Rastrick".
But I am sure the families that appears in the 1841, 1851, and 1861 census are the same - they can be linked by the children, especially George and Emma. The census sheets for 1841 and 1851 show them at "Flowery Fields" (near Hade Edge/Bowshaw - appears on 1854 OS map). 1861 just says "Hade Edge".
Joseph's marriage record gives his father as John Mitchell, delver, and his baptism record John Mitchell, delver, abode Rastrick.
I took the same view as Marmaduke that Fixby and Rastrick aren't that far enough apart, and perhaps it depended on who was giving the information for each census?
I had spotted the neighbouring George Mitchell too, and did a bit of work on him. The interesting thing is to see him living at Magnum Bonum in 1841, as one of the three Mitchell families living there, alongside John Mitchell and another Mitchell family headed by a (slightly younger) James Mitchell. James's family has an elderly Mary Mitchell (age about 70-74). I wondered if she was a parent of one of the others, with the theory that John (b. 1799) and George (b. 1807) might be brothers, with James (b. abt 1817) a son/nephew looking after his grandmother (and John and George's mother?). This would fit with the picture of three closely related Mitchells moving together from the Rastrick area circa 1830 to start up at Magnum Bonum, (John already married, the other two finding spouses nearby and marrying in 1833!) There is a Halifax non-conformist baptism record on IGI for a George Mitchell son of Jonas and Mary Mitchell 9 Feb 1808 which might tie with this and might perhaps be the same Mary, and potentially also John Mitchell's mother.
However, I haven't been able to confirm this, as I haven't been able to find any supporting baptism/marriage records with my limited access to them, and as Holmemoss has already found, there appear to be significant gaps in some of the non-conformist records in the Rastrick/Brighouse area. So it just remains a theory.