He wrote, with his friend William Kirby, Introduction to entomology (1815–1826).
Spence was born in Bishop Burton but little else is known about his early life except that at the age of ten he was in the care of a clergyman who taught him botany. He became interested in entomology when he was 22 and immediately began a correspondence with Kirby. Ten years later he suggested the Introduction to Kirby.
Spence published some 20 notes on entomology.
He was made an 'Honorary English Member' of the Entomological Society at the same time as Kirby was made Honorary Life President and was President 1847-48 and was elected a Fellow of the Royal Society in 1834.