Aims: We perform a multifrequency radio study of the supernova remnant (SNR) G338.3-0.0, in positional coincidence with the TeV source HESS J1640 - 465. We study the morphological and spectral properties of this remnant and its surroundings searching for plausible radio counterparts to the gamma-ray emission. Methods: 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. 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 12CO (J = 1-0) emission line. Results: The new radio observations revealed a remnant with a bilateral morphology, which at 235 MHz has a western wing that is completely attenuated because of absorption caused by foreground ionized gas. The quality of these new images allows us to provide accurate estimates of the total radio flux density of the whole SNR at different radio frequencies. From both these new and existing flux density estimates between 235 MHz and 5000 MHz, we derived for the whole remnant a spectral index α = -0.51 ± 0.06 with a local free-free continuum optical depth at 235 MHz of τ235 = 0.9 ± 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 mJy and 1.0 mJy at 610 MHz 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 its surroundings indicates that there is no associated dense cloud that might explain a hadronic origin for the TeV detection.