Ann, this post of yours is a few years old, but if you are still around ... I always believed John in the 1841 census to be the son of Thomas Turton, the surgeon. John is the same age and does not appear in the 1841 census at home.
I just checked the image of the 1844 Booth /Turton marriage and it quite clearly says his father is Thomas Turton, surgeon, so that proves the above theory nicely! The only way the transcriber could have got Henry is because the registrar first started to write surgeon under Thomas' name instead of in the other column. With the stroke through the 'Su', it does look a bit like Hy, the abbreviated form of Henry.
I am looking into your theory of Martha having two marriages to a Turton. Especially in light of the fact John Turton spent the 1841 census night elsewhere in Moor Top with another woman with a different surname to his. (his looks like Turlow since the T isn't crossed]

ChristineR
Hello Christine
I am also interested in this family (because my grandson is descended from them). I'm starting to think that Martha possibly married two Turton men. Her first son John Turton (born c 1817), a painter, was with his mother Martha in the 1841 census; there is a marriage between John Turton and Margaret Grace Booth which says John's father is HENRY TURTON and Martha is living with husband John Turner in following census records. Of course, it could be a different Martha (there seem to be quite a few Marthas who married a John Turton on the LDS website!).
If you're still around and still interested in this family, I'd love to catch up with you.
Regards
Ann