We present the results of a program of K- and KS-band imaging of a sample of 2 Jy radio galaxies with redshifts 0.03 ≲ z ≲ 0.5, for which the host galaxy morphologies and structural parameters (effective radius, Sérsic index and unresolved nuclear point source contribution) have been determined using galfit. Two-thirds of our sample are best modelled as being hosted by massive elliptical galaxies with Sérsic indices of n = 4-6, with the remainder being better suited either by a mixture of morphological components (usually a bulge plus a small, less luminous, disc component) or by more discy galaxy models with n = 1-2. Our measured galaxy sizes are generally in very good agreement with other imaging programs, both space- and ground-based. We also determine a slightly higher average nuclear point source contribution than similar Hubble Space Telescope based programs. This is due to our inability to separate the active galactic nuclei emission from compact circum-nuclear stellar emission, but does not bias our modelling of the remainder of the host galaxies and our results remain robust. We also observe that roughly half of the objects in our sample are either undergoing major or minor merger activity or are clearly morphologically disturbed.