Rowbotham studied medicine at the University of Manchester and took his degree in 1925. In the 1930s he trained with Geoffrey Jefferson at MRI as a neurosurgeon. In 1936 he was appointed as a neurosurgeon at Stockport Infirmary, Withington hospital and the Christie Hospital. In 1941, he moved to Newcastle, where he built up an internationally renowned department at Newcastle general hospital. He was a former president of the Society of British Neurological Surgeons. in 1944 he published Acute injuries of the head, which became the standard text on the subject. He died on 23 November 1975 aged 76.