Williams was born on 20 July 1860 in Liverpool, England, the son of a businessman. He was educated at Kings College School, London and was expected by his father to continue in the family business. However, his determination to become an artist saw him move to Europe and study under Charles Verlat in Antwerp and later at the Academie Julian. Williams focussed on landscape and marine subjects and painted in oil, pastel and watercolour. He travelled extensively and his impressionistic, luminous paintings sought the transient effects of light and reflections. He was elected a member of the Royal Institute of Painters in Watercolours in 1904. His work was regularly exhibited at the Royal Academy from 1891. He was elected an Associate of the Royal Academy (A.R.A.) on 18 November 1924, a Royal Academician (R.A.) on 14 February 1933, and a Senior R.A. on 1 January 1936. In 1933 he was also elected President of the RI.