Stockdale was born in Branxton, Northumberland. He was an avid intellectual whose education led him to become well acquainted with Greek and Latin classics, nurturing his taste for poetry. After the death of his father financial distress led him to accept the offer of a lieutenancy in the royal Welsh fusiliers. He was forced to leave his position due to ill health in 1757. After his time as a lieutenant he became an ordained deacon in 1759. Starting as a deacon and later taking priest's orders put Stockdale in a good position to extensively explore the world of literature through reading and writing, bringing him into touch with leading intellectuals and poets as well. He was an avidly outspoken reformist. Over the course of his life he witnessed and participated in the great political struggle over slavery and slave trading. Stockdale's "Verses on the abolition of the slave trade" was written in 1804, three years before the bill abolishing the slave trade was finally passed. We find multiple other examples of Stockdale's avid thoughts of the politics of the late 18th century and early 19th century. Stockdale wrote a Letter to Granville Sharp, suggested by the present Insurrection of the Negros in the Island of St. Domingo in 1791. He also published Observations on the Writings and Conduct of our present Political and Religious Reformers in 1792. Stockdale's aggressive poetry, prose and letters, are distinctive examples of his anti-slavery mindset. He died in Lesbury on September 14, 1811.
Stockdale famously eulogized Samuel Johnson's cat Hodge in his "An Elegy on the Death of Dr Johnson's Favourite Cat."