John Sebastian Bach Stopford was born on 25 January 1888 in Hindley Green, Lancashire, the son of Thomas Rinch Stopford and Mary Tyrer (née Johnson). His early education was at Liverpool College and the Manchester Grammar School before proceeding to the University of Manchester in 1906 to study medicine. In 1911 he qualified MB ChB having also won the Dumville Surgical Prize and the Bradley Memorial Scholarship. After qualifying Stopford served briefly as house surgeon to the Rochdale General Infirmary before returning to the University in 1912 as a demonstrator of anatomy. In 1915 he was awarded his MD after submitting a thesis on the blood supply of the brain stem and began lecturing in anatomy that same year.
Stopford specialised in the anatomy of the nervous system and was able to apply his knowledge during WWI in relation to gunshot wounds of the peripheral nerves at the 2nd Western General Hospital. On the departure of Grafton Elliot Smith in 1919 Stopford became professor of anatomy, and so head of the department of anatomy in Manchester, at the age of just 30. He maintained a closer relationship with local hospitals during this time and in 1923 became honorary advisory anatomist to the Manchester Royal Infirmary, a role he held until 1945. He was first appointed to the role of the dean of the medical school in 1923 and held the position until 1927.
From 1928 to 1930 he was pro-vice-chancellor of the university, and from 1931 to 1933 returned to the role of dean. In 1920 he had been made an MBE and 1927 saw him become the first graduate of the Manchester University Medical School to be elected a Fellow of the Royal Society. In 1934 Stopford was invited to become the University's new vice-chancellor, thus making the move from teaching and research to administration. This move wasn't necessarily supported by his colleagues and he himself was reluctant to relinquish his academic role and so retained his role as chair of anatomy until 1937. After this point he held a personal chair of experimental neurology up until 1956.
His other administrative positions were numerous and included chairman of the Universities Bureau of the British Empire; vice-chairman of the Committee of Principals and Vice-Chancellors; chairman-elect of the General Medical Council; chairman of the council of the Royal Manchester College of Music; vice-chairman of the Goodenough Committee; chairman of the Manchester, Salford and Stretford Joint Hospital Advisory Board; chair of the Manchester Regional Hospital Board; and chairman of the Council of the John Rylands Library. Stopford maintained his commitment to medical science throughout his career and published a number of papers in addition to his main work Sensation and the Sensory Pathway (1930). He worked closely with highly-esteemed colleagues such as Sir Harry Platt, Sir Geoffrey Jefferson, Professor E.D. Telford, and Professor John Morley. Stopford's influence and work were widely recognised and he received honorary doctorates from the universities of Leeds, Cambridge, Manchester, Liverpool, and Durham and was also made a fellow of both the Royal College of Physicians (1942) and the Royal College of Surgeons (1955). He retired in 1956 and received a life peerage in 1958 for which he selected Fallowfield as his barony. Long term health problems took their toll and Stopford died on 6 March 1961.