Born in Cronkborne, Isle of Man, the son of a marine engineer, Archibald Knox studied from 1878 to 1884 at the Douglas School of Art, where he subsequently taught towards the end of his career. From 1892 to 1896 Knox was probably attached to Baillie Scott's office in the Isle of Man. In 1897 he moved to London and in 1898 he was attached to the Silver Studio, who marketed some of his textile designs. In about 1898, Knox began to design for Liberty's, to whom he was probably introduced by Baillie Scott, who had designed Liberty textiles in 1893. Liberty's had been importing pewter by Kayser of Krefeld designed by Hugo Leven. Knox designed metalwork to compete with Kayser, the Cymric range of silver from 1899 and the Tudric range of pewter from 1903. Knox's designs used interlaced ornament of a Celtic character; as well as metalwork he designed carpets, textiles and jewellery.

From 1900 to 1904, Knox went back to the Isle of Man, working for the Silver Studio and hence Liberty's on a freelance basis. He then returned to London teaching at various art schools, including that at Kingston, whence he resigned when in 1911 after his methods were criticised as unorthodox by the South Kensington examiners. A group of Kingston students then seceded from the Art School and established the Knox Guild of Craft and Design, which survived until 1939. Knox's style began to go out of fashion in about 1909, when Liberty's sold a number of his metalwork designs to James Connell & Co. He ceased his association with Liberty & Co. in 1912 and went to Philadelphia where he designed carpets for Bromley & Co. He returned to the Isle of man in 1913 and died there in 1933. When Arthur Lasenby Liberty died in 1917, Knox designed his tombstone.