William Hancock's tutor at Glasgow, was James Thomson, an uncle, as James married Anne Hancock, his father sister. James Thomson's brother William Thomson (later Lord Kelvin) was also one of his tutors. Lord Kelvin later endorsed William Hancock's nomination for MInstCE in 1906.

After spending several years working for the Dublin Telephone Exchange, Hancock moved to Western Australia (WA) to take up the appointment of superintendent of telephones (1885). He installed the first phone lines between Government House and the Colonial Secretary's Office and the Perth Exchange, as well as supervising the Perth-Fremantle line works. From 1890 he was supervisor of telegraphs and saw the expansion of lines to the goldfields and remote areas. Hancock was then appointed government electrical engineer and helped establish the tramways system and the installation of submarine cables.

In addition to his full-time government work, William Hancock held many other positions. He was a member of the Senate of the University of Western Australia (1915-1927), honorary radiographer at the Perth Public Hospital (1898-1920) and honorary radiologist at the Fremantle Base Hospital (1915-1920). Fascinated by the newly created X-ray machine, Hancock imported one to WA and began educating medical staff in its uses and operation. Hancock was soon screening patients at the Perth Public Hospital and over the next twenty-two years he carried out an estimated 30, 000+ X-rays. The harm caused by repeated exposure to X-rays was not yet known, so Hancock worked unprotected for all of this time. His hands become severely damaged and disabled forcing his retirement from both the Government and the radiography work (1920). He did, however, stay on as a consulting radiologist at the hospital for a further ten years before returning home.

William Hancock's major contributions to the health of the people of WA and to the state's infrastructure were recognised in 1924 when he was appointed the inaugural Kelvin gold medallist by the Royal Society (WA). Further accolades came posthumously and include a commemorative stained glass window in Winthrop Hall at the University of Western Australia (1934) and a memorial plaque at the Institute of Anatomy in Canberra.