William Brockbank was the son of Edward Mansfield Brockbank. He was educated at Cambridge and Manchester Universities. He qualified in medicine in 1924, and thereafter worked at MRI, and Cheadle Royal Hospital. From 1929-32 he was honorary physician at Manchester Jewish hospital, and medical officer to outpatients at MRI. In 1932, he was appointed honorary assistant physician (later full physician) at MRI. From 1948 until his retirement he was a consultant physician. He was dean of clinical studies at MRI from 1939-1965, and headed its asthma clinic from 1946-1965. Brockbank lectured in medical subjects for many years at the University of Manchester. He served with the RAMC during the War, reaching the rank of lieutenant colonel.
Like his father, Brockbank was a medical historian. He published Portrait of a hospital [a history of the MRI] (1952); The honorary medical staff of the Manchester Royal Infirmary, 1830-1948 (1965); The Diary of Richard Kay (as editor), (1968); Nursing at the Manchester Royal Infirmary, 1752-1929 (1970), as well as numerous articles. Brockbank was also honorary archivist at the MRI from 1965-1977, and honorary medical archivist, later honorary archivist and keeper at John Rylands University Library of Manchester, 1965-1984. He helped maintain the Manchester Medical Collection, and organised a variety of exhibitors on medical themes at the University. Brockbank was, like his father, chairman of the University's medical library committee, from 1951-1954.
Brockbank was active in the Manchester Medical Society; he was chairman of the committee that enacted the amalgamation of the various Manchester medical societies in 1950, was president of the section of medicine in 1953-4, and president of the Society in 1955-6.
William Brockbank died on 12 March 1984.