Edward Brockbank was born at Geelong, Australia in 1866, the son of a metal merchant. The family removed to Britain was Edward was four, and he was educated at Bootham School, York, and Owens College. He qualified MB ChB in 1890, and took his MD three years later. He held various posts at MRI, Manchester Children's Hospital and Ancoats, before being elected to the honorary staff of MRI in 1905. He was a lecturer in materia medica and clinical medicine at the University of Manchester, and was dean of clinical studies at MRI from 1913-1921. Brockbank was also chairman of the research sub-committee of the Manchester Committee on Cancer from 1925-39. He was a medical referee for many years. He was active in the Manchester Medical Society , serving as chairman of its Medical Library Committee from 1906-30, and was chairman of the University of Manchster Medical Library Committee from 1930-51, following the incorporation of the Manchester Medical Society library into the University Library. Brockbank's clinical interests were in cardiology, and he helped establish with A.V. Hill, the department of electrocardiography at MRI.
Brockbank was a noted medical historian; he was the historian of the MRI, and wrote Sketches of the lives and work of the honorary staff of the Manchester Infirmary 1752-1830 (1904), A centenary history of the Manchester Medical Society (1934), A short history of Cheadle Royal (1934), and The foundations of provincial medical education in England (1936). As chairman of the Library Committee, he assisted Bosdin Leech in the creation of the Manchester Medical Collection. He was president of the Manchester Medical Society in 1923-4. He was the father of William Brockbank.