Since I posted I think I've found the right parents, but would appreciate your input.
i believe his parents were John Turnbull and Barbara Bailey and that he was born in Sherburn in June 1843.
In turn I believe John's parents were Matthew and Mary Dawson, and that he was born 1802 in Oxclose.
I have struggled to find John and Barbara's marriage record, but believe they may have married 1829 in Bishopwearmouth.
I am descended from William's daughter Sarah Catherine Roland Wilson Turnbull (never got to the bottom of where the Roland and Wilson names come from...) and her daughter Elizabeth Cooper (my grandmother).
Would love to hear any confirmation or otherwise from you, barely touched my tree in a couple of years as I have young children, but would love to get back into it - just need the time!