Born in Anglesey, the son of a Wesleyan minister, Dodd trained at the Glasgow School of Art alongside  Sir Muirhead Bone who married Dodd's sister. While at Glasgow, Dodd won the Haldane Scholarship in 1893 allowing him to travel around France, Italy and  Spain, returning to England in 1895. After a period working and teaching in Manchester he moved to Blackheath, London in 1904 and in 1916 was appointed an official war artist by the War Propaganda Bureau who sent him to the Western Front to paint a collection of portraits later published as ‘Generals of the British Army’ soon followed up by ‘Admirals of the British Navy’. In peacetime he worked as a curator at the Tate becoming a trustee in 1929, a position he held for the next six years. His portrait of Virginia Woolf is amongst many of his works held at the National Portrait Gallery. The Imperial War Museum, the British Museum and the Walker Art Gallery in Liverpool all hold his work.