In 1799, he entered Peterhouse, Cambridge and then University College, Oxford, where he graduated Bachelor (1803) and Master of Arts (1806).
He became a Fellow and Tutor at University College, Oxford, in 1806, deacon in 1806 and priest in 1807. He then became rector of Ryton in 1811, joining a prestigious group with previous rectors including Thomas Secker, later Archbishop of Canterbury. After his time as rector at Ryton, he became Canon (1829) and then Archdeacon of Durham in 1831 and, a year later, became the first warden of the University of Durham.
Thorp remained heavily involved with the university, also being the first master, the most senior person in the SCR, of University College.
This was a position he held until his death in Durham in 1862. He was buried at Ryton Church.