Following the study already presented in our previous work, based on the Nordic Optical Telescope (NOT) sample, which consists on five clusters of galaxies within the redshift range 0.15$<$z$<$0.25, imaged within the central 0.5-2 Mpc in very good seeing conditions, we have studied the quantitative morphology of their bright galaxy population. The surface brightness profiles of the galaxies have been decomposed in the bulge and disc photometrical components. Previously, we have performed simulations in order to check the reliability of the fits. These data allow us to derive a quantitative morphological classification of the galaxies, which has been compared with the previous visual one. Galaxies in clusters at this range of redshift do not present appreciable evolution for the bulges scales. However, their disc scales are different from those galaxies placed in clusters at low redshift and more similar to the field galaxies at low redshift. This result suggests that the evolution of the disc component in galaxy clusters is faster than in field ones. Fast galaxy-galaxy encounters or interactions with the global gravitational potential are pointing to be the mechanisms responsible of this evolution in the last 2.5 Gyr.