Self-interstitial cluster diffusivity in Fe-Cr alloys is known to be reduced in a non-monotonic way as a function of Cr concentration. This non-monotonic behaviour correlates well with the experimentally observed swelling in these alloys, under comparable irradiation conditions. Moreover, recent studies reveal that C atoms dispersed in the Fe matrix form under irradiation complexes with vacancies which, in turn, act as trap for onedimensionally migrating self-interstitial clusters. The mobility of one-dimensional migrating clusters is considered key to determine swelling susceptibility. In this work we developed physically-based sets of parameters for object kinetic Monte Carlo simulations intended to study the nanostructure evolution under irradiation in Fe-Cr-C alloys, neutron irradiated up to ~0.6 dpa at 563 K. Our model shows that the SIA cluster reduced mobility has a major influence on the nanostructural evolution: it increases the number of vacancy-SIA recombinations and thus leads to the suppression of voids formation. This provides a clear framework to interpret the non-monotonic dependence of swelling in Fe-Cr alloys versus Cr content. Our model also suggests that the amount of C in the matrix has an equally important role: high amounts of it may counteract the beneficial effect that Cr has in reducing swelling.