We present the first results of our Hubble Space TelescopeHST WFPC2 F814W snapshot imaging survey, targeting virtually all sub-mJy decimetric radio-selected star-forming galaxies. The radio selection at ∼1 GHz is free from extinction effects and the radio luminosities are largely unaffected by AGN contamination, making these galaxies ideal tracers of the cosmic star formation history. A subsample of four targets is presented here, selected at 1.4 GHz from the spectroscopically homogenous and complete samples of Benn et al. and Hopkins et al. The redshifts are confined to a narrow range around z∼0.2, to avoid differential evolution, with a radio luminosity close to L∗ where the galaxies dominate the comoving volume-averaged star formation rate. We find clearly disturbed morphologies resembling those of ultraluminous infrared galaxies, indicating that galaxy interactions may be the dominant mechanism for triggering star formation at these epochs. The morphologies are also clearly different from those of coeval quasars and radio galaxies, as found in star-forming galaxies selected at other wavelengths. This may prove challenging for models that propose direct causal links between AGN evolution and the cosmic star formation history at these epochs. The asymmetries are typically much larger than seen in the Canada–France Redshift Survey at similar redshifts, optical luminosities and Hα-derived star formation rates, indicating the possible existence of an obscuration-related morphological bias in such samples.