At the StockholmOlympics, Applegarth was eliminated in the semifinals of 100 m competition and won a bronze medal in 200 m. As the anchoring leg in the British 4x100 m relay team, he won a gold medal, in spite of finishing second after the United States in the semifinal. The United States was later disqualified for a fault in passing the baton; the same mistake was made in the final by world record holder and main favourite German team.
Applegarth was a British AAA champion in 100 yd (91 m) in 1913 and 1914 and in 220 yd (200 m) from 1912 to 1914. Shortly after the Olympics, Applegarth repeated the Donald Lippincott's world record in 100 m of 10.6 and set a new world record of 21.2 in 200 m in the 1914 AAA meeting. His 200 m record was not broken until 1928.
In 1915, Applegarth turned professional and emigrated to America, where became track and soccer coach at Mercersburg Academy in Pennsylvania. He also played for Brooklyn in the American Soccer League. William Applegarth died at age 68, in the same year that his British 100 yd (91 m) record of 9.8 was finally broken.