St Bartholomew's Hospital
Jessop joined the staff of St Bartholomew's Hospital (1882). He became Senior Demonstrator in anatomy at St Bartholomew's Hospital (1882–94), Hunterian Professor of comparative anatomy and physiology (1887-8) and was subsequently Ophthalmic Surgeon to the Western General Dispensary, to the Foundling Hospital and to the Children's Hospital at Paddington Green. He was made Senior Ophthalmic Surgeon at St Bartholomew's Hospital in 1901.