After receiving an M.S. in physics from the University of Manchester in 1931, Parker became a medical physicist at the Christie Hospital and the Holt Radium Institute in Manchester. With James R. Paterson, he developed in 1932 the Paterson-Parker method, or Manchester System, for radiation therapy. The method allows physicians to use radium needles or tubes to maximize the radiation dose delivered to a cancerous tumour whilst minimizing the dose to healthy tissue. In 1938 Parker immigrated to the U.S.A. to begin work at the Swedish Hospital in Seattle, where he worked with the radiologist Simeon T. Cantril on Supervoltage Therapy research at the Tumor Institute. In 1942 Parker went to the University of Chicago to work on the Manhattan Project at the Metallurgical Laboratory. In 1943 he went to Clinton Engineer Works to establish the health physics program for the U.S. atomic energy program. In 1944 Parker returned to the state of Washington to initiate the health physics program at the Hanford Engineer Works. In 1947 he became manager of operations and research in radiological science. In 1956 he was promoted to become the overall manager at the Hanford Laboratories, holding this position until 1965 when operation of Hanford Laboratories was transferred from GE to Battelle Memorial Institute.