Aims: Following the study presented in our previous paper, based on the Nordic Optical Telescope (NOT) sample, which consists of five clusters of galaxies within the redshift range 0.18 ≤ z ≤ 0.25 imaged in the central 0.5-2 Mpc in very good seeing conditions, we have studied the quantitative morphology of their bright galaxy population Methods: We analyzed the surface brightness profiles of the galaxy population in those clusters, after performing simulations in order to check the reliability of the fits. We also derived a quantitative morphological classification. Results: The structural parameters derived from these analyses are presented. We obtained that the structural parameters of E/S0 galaxies are similar to those shown by galaxies in low redshift clusters. However, the disc scales are different. In particular, the scales of the discs of galaxies in medium redshift clusters are statistically different than those located in similar galaxies in the Coma cluster. However, the scales of the discs of galaxies in medium redshift clusters are similar to nearby field galaxies. Conclusions: Our results suggest that the evolution of the disc component of galaxies in clusters is faster than in field ones. Mechanisms like galaxy harassment showing timescales of ˜ 1 Gyr could be responsible for this disc scale evolution. This indicates that spiral galaxies in clusters have undergone a strong evolution in the last 2.5 Gyr or that Coma is in some way anomalous.