Obtaining redshifts for radio galaxies can be difficult as their continuum spectra are essentially featureless and significant detections of the redshifted HI 21cm line are expected for only a small fraction of sources. Here, we show that useful information can still be gained on the redshift of galaxies detected in radio continuum surveys, even without the formal detection of HI spectral line emission. We use only the relatively weak priors that we know a galaxy's location on the sky (i.e. from the continuum detection) and that the galaxy has a physical value for velocity dispersion (restricting the width of lines which we are searching for). This enables us to construct a very simple redshift estimation algorithm which, when applied to a realistic population of galaxy lines observed with an SKA1-MID-like experiment, gives redshift estimates with error distributions comparable to that typical for optical/near-IR photometric redshift estimators for up to 100% of the star-forming galaxies. We also discuss how such an estimator could be further improved by use of more prior information from the continuum image such as a galaxy's size, shape and surface brightness.