Harriman was born at Maryport, Cumberland, into a family of German background named Hermann.
became a medical student at 17; but after two years returned to classical studies, and then took holy orders.
He moved on to Barnard Castle, Egglestone, and Gainford in County Durham, Long Horseley in Northumberland, Heighington and Croxdale, and lastly to the perpetual curacy of Satley, Durham.
He furnished plants for James Edward Smith's English Botany such as Bartsia alpina, which he had gathered in Teesdale.
He was the first botanist to find Gentiana verna in England, and other rare plants in Westmorland and Cumberland.