Schäfer, the son of a city merchant in London, qualified in medicine at University College there in 1874. He joined the staff of the college and served as Jodrell Professor of Physiology from 1883 until 1899. He then moved to a similar chair at the University of Edinburgh where he remained until his retirement in 1933.

In 1896 Schäfer, working with George Oliver, discovered that an extract from the medulla of the adrenal gland produced an immediate elevation of blood pressure when injected into animals. The substance, adrenaline (epinephrine), was later isolated and crystallized by Jokichi Takamine in 1901. Schäfer also worked on pituitary extracts. He is further remembered in the field of endocrinology for his proposal that the active pancreatic substance in the islets of Langerhans should be called ‘insuline’, some eight years before its discovery by Frederick Banting and Charles Best.

Schäfer published two influential works: Essentials of Histology (1885) and Endocrine Organs (1916). He also founded the important Quarterly Journal of Experimental Physiology in 1898.

Schäfer had named one of his two sons Sharpey after his much admired anatomy teacher, William Sharpey, at University College. But after the tragic death of both his sons in World War I Schäfer changed his own name to the hyphenated Sharpey-Schäfer.