Born on 10 October 1857 in Bristol (GRO), Arthur attended a Quaker School at Weston Super Mare, where he became friends with, amongst others, Henry Scott TUKE (aka 'Harry'). By the time he was in London with the idea of a business career, Tuke was also in London, entering the Slade to begin formal art training. They travelled abroad together with other friends, notably the Gotches, and Tanner decided also to become an artist.

A bachelor, reputedly with a private income, he was one of the first artists to settle in West Cornwall, where he lived at Cappy cottage, Lamorna, and abroad when funds were low. In the summer of 1887 he is described by Lomax as the protégé of Phil Whiting, camping out with him and Tuke, walking and sailing in his boat. A photograph from the Birch family album is included in Lomax (p86). In 1889 he spent time abroad in France, studying at Julian's Academie in Paris. Until his death he remained one of Tuke's closest friends and an active member of the Lamorna and Newlyn communities. Tanner died on 6 April, 1916, age 58, at Bristol (GRO).