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 (0.8 × 1010 M⊙ < M⋆ < 4 × 1010 M⊙) 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 Sérsic-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.