In 1792 Alexander went to China as a draughtsman attached to Lord Macartney's embassy. The other official artist was Thomas Hickey. Alexander returned two years later with many sketches, some of which were used to illustrate Sir George Staunton's account of the embassy (1794) and Sir John Barrow's Travels in China (1804). Local Chinese craft and their inhabitants were a favourite. This example, one of two in the Museum's collection, is signed and dated 1793.

Alexander became Professor of Drawing at the Military College at Great Marlow in 1802. He relinquished this post in 1808 on being appointed Keeper of Prints and Drawings at the British Museum.