Context : Aims : To perform a multifrequency radio study of the supernova remnant ( SNR ) G338.3 - 0.0 , in positional coincidence with the TeV source HESS J1640 - 465 . To study the morphological and spectral properties of this remnant and its surroundings searching for plausible radio counterparts to the gamma-ray emission . Methods : To carry out this research we observed the SNR G338.3 - 0.0 using the Giant Metrewave Radio Telescope ( GMRT ) at 235 , 610 , and 1280 MHz . We also reprocessed archival data from the Australia Telescope Compact Array ( ATCA ) at 1290 and 2300 MHz . Also we conducted a search for radio pulsations towards a central point-like source , using the GMRT antennas at 610 and 1280 MHz . The molecular material in the region of the SNR was investigated based on observations made with the NANTEN telescope in the ^ { 12 } CO ( J=1-0 ) emission line . Results : The new radio observations revealed a remnant with a bilateral morphology , which at 235 MHz has the western wing completely attenuated because of absorption due to foreground ionized gas . The quality of the new images allows us to provide accurate estimates for the total radio flux density of the whole SNR at different radio frequencies . From the new and existing flux density estimates between 235 and 5000 MHz we derived for the whole remnant a spectral index \alpha = -0.51 \pm 0.06 with a local free-free continuum optical depth at 235 MHz \tau _ { 235 } = 0.9 \pm 0.3 . No radio pulsations were detected towards the only radio point-like source within the HESS error circle . We derived upper limits of 2.0 and 1.0 mJy at 610 and 1280 MHz , respectively , for the pulsed flux towards this source . No radio counterpart was found for the pulsar wind nebula discovered in X-rays . The inspection of the interstellar molecular gas towards G338.3 - 0.0 and surroundings revealed that there is not any associated dense cloud that might explain a hadronic origin for the TeV detection . Conclusions :