The temperature dependent internal friction spectra of cold-worked and neutron irradiated iron and iron–copper binary alloys are investigated. By increasing dose, both c- and Snoek-Köster-relaxation peaks exhibit strong shift towards low temperatures, as a consequence of the reduction of double kink activation energy. This shift is found to be the largest in alloys with the highest copper content. Besides, new modes appear in the spectra at energies of about 410 and 540 K. The 410 K peak intensity increases at the expense of Snoek-Köster peak intensity, indicating that redistribution of carbon takes place under irradiation, most probably as a result of grain boundary segregation. The presence of copper impedes the carbon redistribution by influencing the formation of carbon-vacancy complexes, which causes the grain boundary segregation, and activation of the 410 K relaxation process at larger neutron fluence in comparison with pure iron.