About 20 per cent of all nearby early-type galaxies (M-star greater than or similar to 6 x 10(9)M(circle dot)) outside the Virgo cluster are surrounded by a disc or ring of low-column-density neutral hydrogen (H I) gas with typical radii of tens of kpc, much larger than the stellar body. In order to understand the impact of these gas reservoirs on the host galaxies, we analyse the distribution of star formation out to large radii as a function of HI properties using GALEX UV and SDSS optical images. Our sample consists of 18 HI-rich galaxies as well as 55 control galaxies where no HI has been detected. In half of the HI-rich galaxies, the radial UV profile changes slope at the position of the HI radial profile peak. To study the stellar populations, we calculate the FUV-NUV and UV-optical colours in two apertures, 1-3 and 3-10 R-eff. We find that HI-rich galaxies are on average 0.5 and 0.8 mag bluer than the HI-poor ones, respectively. This indicates that a significant fraction of the UV emission traces recent star formation and is associated with the HI gas. Using FUV emission as a proxy for star formation, we estimate the integrated star formation rate in the outer regions (R > 1R(eff)) to be on average similar to 6 x 10(-3) M-circle dot yr(-1) for the HI-rich galaxies. This rate is too low to build a substantial stellar disc and, therefore, change the morphology of the host. We find that the star formation efficiency and the gas depletion time are similar to those at the outskirts of spirals.