Extended ultraviolet (XUV) discs have been found in a substantial fraction of late-type - S0, spiral and irregular - galaxies. Similarly, most late-type spirals have an extended gas disc, observable in the 21-cm radio line (HI). The morphology of galaxies can be quantified well using a series of scale-invariant parameters; concentration-asymmetry-smoothness (CAS), Gini, M_20_, and G_M_ parameters. In this series of papers, we apply these to HI column density maps to identify mergers and interactions, lopsidedness and now XUV discs. In this paper, we compare the quantified morphology and effective radius (R_50_) of the Westerbork observations of neutral Hydrogen in Irregular and SPiral galaxies Project (WHISP) HI maps to those of far- and near-ultraviolet images obtained with GALEX, to explore how close the morphology and scales of HI and UV in these discs correlate. We find that XUV discs do not stand out by their effective radii in UV or HI. However, the concentration index in far-ultraviolet (FUV) appears to select some XUV discs. And known XUV discs can be identified via a criterion using asymmetry and M_20_; 80 per cent of XUV discs are included but with 55 per cent contamination. This translates into 61 candidate XUV disc out of our 266 galaxies, 23 per cent consistent with previous findings. Otherwise, the UV and HI morphology parameters do not appear closely related.