It is not known when Robert Dudley began his career as an artist, but by 1849, at age 23, he was Hon. Secretary of the New Society of Painters in Water Colours. Although he also produced wood engravings, lithographs, and oil paintings, as well as designing book covers, watercolour remained his preferred medium.

At the 1851 Crystal Palace Exhibition, he was superintendent of the restorations and monuments, and principal draughtsman for the Mediaeval Court, which was designed and arranged by architect M. Digby Wyatt. In 1857 Dudley was “the youngest of the art directors” at the Manchester Art Treasures Exhibition. He was Special Artist to the Illustrated London News during the 1860s, and was engaged by Day & Son to illustrate many of their lithographed picture books.

Perhaps his best-known works are the approximately seventy watercolours and oil paintings he made to illustrate the 1865 and 1866 Atlantic Cable expeditions, for which he sailed on Great Eastern in both years. 24 of the watercolours were reproduced as coloured lithographs in the 1866 book “The Atlantic Telegraph” published by Day & Son. The Science Museum has seven of his watercolours from this series, as well as examples of the published lithographs, and others are in museum and archive collections in North America and Britain.

As well as his illustration work, Dudley also produced fine art. He showed 47 paintings between 1865 and 1891 at London venues, including 24 at the Royal Academy and others at the New Water-Colour Gallery, Suffolk Street, and various exhibitions. Towards the end of that period he also wrote and illustrated a number of his own books for children, and created art for Christmas cards, many with an anthropomorphic theme.