We report on a comparative study of the low temperature emission and polarisation properties of InGaN/GaN quantum wells grown on nonpolar (11$\bar 2$0) $a$-plane and (10$\bar 1$0) m-plane free-standing bulk GaN substrates where the In content varied from 0.14 to 0.28 in the m-plane series and 0.08 to 0.21 for the a-plane series. The low temperature photoluminescence spectra from both sets of samples are broad with full width at half maximum height increasing from 81 to 330 meV as the In fraction increases. Photoluminescence excitation spectroscopy indicates that the recombination mainly involves strongly localised carriers. At 10 K the degree of linear polarisation of the $a$-plane samples is much smaller than of the $m$-plane counterparts and also varies across the spectrum. From polarisation-resolved photoluminescence excitation spectroscopy we measured the energy splitting between the lowest valence sub-bands to lie in the range of 23–54 meV for the $a$- and $m$-plane samples in which we could observe distinct exciton features. Thus the thermal occupation of a higher valence sub-band cannot be responsible for the reduction of the degree of linear polarisation at 10 K. Time-resolved spectroscopy indicates that in $a$-plane samples there is an extra emission component which is at least partly responsible for the reduction in the degree of linear polarisation.