There were two Bethuel Haycocks. The elder Bethuel (1766-1839) was my 4th great grandfather. He had, among other children, John, born in 1809, and my 3rd great grandfather, Bethuel. I'm guessing that the John born in 1809 was the father of your John, born in 1843. The younger Bethuel had a son John who was my 2nd great grandfather. He emigrated to the US ~1864. So our common ancestor would be the elder Bethuel.
Bill