Burgess was born at Stretford and educated at Owens College, where he enjoyed a very successful academic career. He took a M.Sc in physiology in 1895 and the MB in 1896. His early appointments were at MRI, Crumpsall and Manchester Children's Hospital; he was elected honorary assistant surgeon at MRI in 1905. During the First World War he was on the staff of the 2nd Western General Hospital. He also worked at the Christie Hospital. In 1921 he was made professor of surgery at the University of Manchester, and remained in this post until 1934. He was president of the BMA in 1929, and president of the Association of Surgeons in 1934. He delivered the Hunterian Oration to the College of Surgeons in 1941. Burgess was known as a skilled surgeon, with a large practice in the North West of England. He was a former president of the Manchester Medical Society and Manchester Surgical Society. He introduced full aseptic dress to operating theatres in Manchester.