We use the Herschel-ATLAS survey to conduct the first large-scale statistical study of the submillimetre properties of optically selected galaxies. Using ~80000 r-band selected galaxies from 126deg^2^ of the GAMA survey, we stack into submillimetre imaging at 250, 350 and 500um to gain unprecedented statistics on the dust emission from galaxies at z<0.35. We find that low-redshift galaxies account for 5 per cent of the cosmic 250-um background (4 per cent at 350um; 3 per cent at 500um), of which approximately 60 per cent comes from 'blue' and 20 per cent from 'red' galaxies (rest-frame g-r).