Wilkinson studied science and medicine at Owens College Manchester. He qualified LSA in 1876 and MRCS in 1877, and he also took the London MB in the same year. In 1880 he received the MD from the University of London. For several years he was in general practice in Oldham and Stockport. In 1880 he became assistant medical officer at MRI. In 1892 he was appointed honorary assistant physician at MRI and remained on the staff until 1913. Wilkinson was well regarded as a clinical teacher, and was dean of clinical education at MRI.
Wilkinson's main area of interest was renal disease. Outside medical practice, Wilkinson was a Methodist lay preacher and he wrote religious verse and hymns. He was a former president of the Manchester Medical Society, the Pathological Society and the Manchester Clinical Society.