Crompton was the grandson of his namesake, the inventor of the spinning mule. He qualified in 1839 after serving an apprenticeship under Fawdington, and worked as a general practitioner in Manchester. Active in the Manchester Medical Society , he was secretary in 1843 and 1856-8, and president in 1860. Crompton was also a surgeon at Salford Royal Hospital. He was interested in the welfare of the blind, and was surgeon to Henshaw's Blind Asylum, Manchester.