We study the influence of environment on the structure of disc galaxies, using IMFIT to measure the g- and r-band structural parameters of the surface-brightness profiles for ~700 low-redshift (z<0.063) cluster and field disc galaxies with intermediate stellar mass (0.8x10^10^M_{sun}_<M*<4x10^10^M_{sun}_) from the Sloan Digital Sky Survey, DR7. Based on this measurement, we assign each galaxy to a surface-brightness profile type (Type I = single-exponential, Type II = truncated, Type III = antitruncated). In addition, we measure (g-r) rest frame colour for disc regions separated by the break radius. Cluster disc galaxies (at the same stellar mass) have redder (g-r) colour by ~0.2 mag than field galaxies. This reddening is slightly more pronounced outside the break radius. Cluster disc galaxies also show larger global Sersic-indices and are more compact than field discs, both by ~15 per cent. This change is connected to a flattening of the (outer) surface-brightness profile of Type I and - more significantly - of Type III galaxies by ~8 per cent and ~16 per cent, respectively, in the cluster environment compared to the field. We find fractions of Type I, Type II and Type III of (6+/-2) per cent, (66+/-4) per cent and (29+/-4) per cent in the field and (15_-4_^+7^) per cent, (56+/-7) per cent and (29+/-7) per cent in the cluster environment, respectively. We suggest that the larger abundance of Type I galaxies in clusters (matched by a corresponding decrease in the Type II fraction) could be the signature of a transition between Type II and Type I galaxies produced/enhanced by environment-driven mechanisms.