William Alexander studied under William Pars and J. C. Ibbetson before joining the Royal Academy Schools in 1784. He was appointed as one of the draughtsmen to join Lord McCartney's embassy to China, which set sail in 1792. For two years he filled his sketch books with landscapes, figure subjects and events which he was able to use to good advantage on his return to England, illustrating Sir George Staunton's account of the Embassy (1797), and also Sir John Barrow's Travels in China (1804). He also published his own works on the subject of China in 1798, and a book on the dress and manners of the Chinese in 1814. He was appointed professor of drawing at the military college of Great Marlow. In 1808 he became keeper of prints and drawings at the British Museum, a position that he kept until his death. In addition to painting English landscapes, he also drew detailed drawings of antiquities.