I think it would be best to make sure of Martha's maiden name by getting a birth certificate of one of her children.
Then if the marriage at St Peter's is the right one you could try looking at the actual entry to see if it gives any more information - sometimes it will state father's names or where the people lived and that can help narrow the field.
That said, it looks to me as though Martha is a second wife as she is born 1819 but the eldest child is born 1833 which would make Martha on the young side. It looks likely to me that Mary is a child of an earlier marriage and then Ellen is the first child of Richard and Martha.
That being so then a marriage 1837-1838 is likely. There is one for Richard Crowther reg at Bradford Sep qtr 1837. Two possible Marthas listed but one has the surname Harrison so I think it likely that is the right one since Harrison is the middle name of one of the boys in the 1851 census.
So, I suggest that you chose one of the children of Martha and Richard, get the birth certificate and find Martha's maiden name. If it turns out to be Harrison get the marriage certificate from 1837 and that should give you father's names and occupations for both Richard and Martha. Then you can perhaps go back to the 1841/51 census and see if Mr Crowther snr was still alive and take it from there
