I've had a load of success with high-thread-count (pure) cotton sheets/pillowcases. Above 500 threads/inch the material looks and feels like scaled canvas.
DO wash the material as hot as you can to remove any chemicals/treatment, and to help pre-shrink it.
DO dye anything white with a splash of Dylon (a yellow/sand sort of colour) to knock the white off and make it more canvas-like.
Stitch it up, wash (cooler this time), tumble and then iron it.
Andy