Here we demonstrate the effect of dielectric and plasmonic nanoparticles on the random lasing behaviour of a polymer optical fibre coated with an organic dye, Rh-640- perchlorate. Coherent random lasing was observed both in the presence of ZnO nanorods and Au nanourchins upon transverse optical pumping using a Q-switched Nd: YAG laser. With the same particle density, a significant reduction in the lasing threshold was observed in the case of the plasmonic random laser. The polymer optical fibre was fabricated using a custom-made fibre drawing tower, and the random lasing media was coated on its surface by the dip-coating method. The present analysis demonstrates that the combined effect of scattering by the nanoparticles and the cylindrical fibre geometry is responsible for the low threshold coherent random laser.