The continued interest in the study of radiative neutron capture on atomic nuclei is due, on the one hand, to the important role played by this process in the analysis of many fundamental properties of nuclei and nuclear reactions, and, on the other hand, to the wide use of the capture cross-section data in the various applications of nuclear physics and nuclear astrophysics, and, also, to the importance of the analysis of primordial nucleosynthesis in the Universe. This paper is devoted to the description of results for the processes of the radiative neutron capture on certain light atomic nuclei at thermal and astrophysical energies. The consideration of these processes is done within the framework of the potential cluster model (PCM), general description of which was given earlier. The methods of usage of the results obtained, based on the phase shift analysis intercluster potentials, are demonstrated in calculations of the radiative capture characteristics. The considered capture reactions are not part of stellar thermonuclear cycles, but involve in the basic reaction chain of primordial nucleosynthesis in the course of the Universe formation.