Context : Aims : We present a radio morphological study and spectral analysis for a sample of 13 cD galaxies in rich and poor clusters of galaxies . Methods : Our study is based on new high sensitivity Giant Metrewave Radio Telescope ( GMRT ) observations at 1.28 GHz , 610 MHz and 235 MHz , and on archival data . From a statistical sample of cluster cD galaxies we selected those sources with little information available in the literature and promising for the detection of aged radio emission . Beyond the high sensitivity images for all 13 radio galaxies , we present also a detailed spectral analysis for 7 of them . Results : We found a variety of morphologies and linear sizes , as typical for radio galaxies in the radio power range sampled here ( low to intermediate power radio galaxies ) . The spectral analysis shows that 10/13 radio galaxies have steep radio spectrum , with spectral index \alpha \geq 1 . In general , the radiative ages and growth velocities are consistent with previous findings that the evolution of radio galaxies at the cluster centres is affected by the dense external medium ( i.e . low growth velocities and old ages ) . We suggest that the dominant galaxies in A 2622 and MKW 03s are dying radio sources , which at present are not fed by nuclear activity . On the other hand , the spectacular source at the centre of A 2372 might be a very interesting example of restarted radio galaxy . For this source we estimated a life cycle of the order of 10 ^ { 6 } yr . Conclusions :