We present the results of our investigation into the stellar populations of 24 radio galaxies at z ~= 0.5 drawn from four complete, low-frequency-selected radio surveys. We use the strength of the 4000-Å break as an indicator of recent star formation and compare this with radio luminosity, optical spectral classification and morphological classification. We find evidence of different star formation histories for high- and low-luminosity radio sources; our group of low radio luminosity sources (typically Fanaroff-Riley type I sources) has systematically older stellar populations than the higher radio luminosity group. Our sample is also fairly well divided by optical spectral classification. We find that galaxies classified as having low excitation spectra (LEGs) possess older stellar populations than high excitation line objects (HEGs), with the HEGs showing evidence for recent star formation. We also investigate the link between radio morphology, as used by Owen and Laing, and the stellar populations. We find that there is a preference for the `fat-double' sources to have older stellar populations than the `classical double' sources, although this is also linked to these sources lying predominantly in the LEG and HEG categories, respectively. These results are consistent with the hypothesis that HEGs are powered by accretion of cold gas, which could be supplied, for example, by recent mergers, secular instabilities or filamentary cold flows. These processes could also trigger star formation in the host galaxy. The host galaxies of the LEGs do not show evidence for recent star formation and an influx of cold gas and are consistent with being powered by the accretion of the hot phase of the interstellar medium.