Burke was born in 1906 in Liverpool. During the 1920s and 30s he studied art at Liverpool College of Art and the Royal College of Art, London.
In 1941 he joined the Merchant Navy as 3rd Radio Officer on the ship the Dalesman. In May that year, the Dalesman was bombed and sunk by enemy aircraft off the coast of Crete. Burke, along with other Merchant Navy personnel, was transferred to Milag (Marine Internierten Lager, or Marine Internment Camp) at Westertimke, north west Germany. Whilst imprisoned, he produced many drawings and watercolours. These included images of camp life, portraits and set designs for theatrical productions.
In 1945, Burke was repatriated to Britain. He died the same year, probably of blackwater fever which he had contracted in the camps.