Radio AGN in the nearby Universe are more likely to be found in galaxies with early-type morphology, the detection rate in spiral or late-type galaxies (LTGs) being around an order of magnitude lower. We combine the mJy Imaging VLBA Exploration at 20cm (mJIVE-20) survey with the Sloan Digital Sky Survey (SDSS), to study the relatively rare population of AGN in LTGs that have nuclear radio luminosities similar to that in their early-type counterparts. The LTG AGN population is preferentially hosted by galaxies that have high stellar masses (M* > 10^10.8 MSun), red colours and low star-formation rates, with little dependence on the detailed morphology or local environment of the host LTG. The merger fraction in the LTG AGN is around 4 times higher than that in the general LTG population, indicating that merging is an important trigger for radio AGN in these systems. The red colours of our systems extend recent work which indicates that merger-triggered AGN in the nearby Universe appear after the peak of the associated starburst, implying that they do not strongly regulate star formation. Finally, we find that in systems where parsec-scale jets are clearly observed in our VLBI images, the jets are perpendicular to the major axis of the galaxy, indicating alignment between the accretion disc and the host galaxy stellar disc.