It has been claimed by Taylor et al. that the low-redshift end of the K-z r
elation for radio galaxies is too bright by about half a magnitude owing to
contributions from the obscured quasar nuclei. Such a result has major imp
lications for the use of the K-band Hubble diagram in understanding the cos
mological evolution of radio galaxies. In this paper we present 1-5-mum ima
ging data of a nearly complete sample of low-redshift radio galaxies; this
approach allows us to determine accurately the strengths of any unresolved
nuclear components in the galaxies. We detect nuclear sources in five targe
ts, whose broad-band colours are consistent with reddened quasar spectra. I
n all the five cases the ratio of the inferred intrinsic near-infrared lumi
nosity to the narrow-line luminosity is typical of quasars. We find a corre
lation between the inferred nuclear extinction and core-to-lobe ratio, whic
h places constraints on the geometry of the torus. We find evidence for a s
hift of the K-z relation to fainter magnitudes, but by a much smaller amoun
t (similar to0.1 mag) than determined by Taylor et al. Under the assumption
that the nuclear sources in radio galaxies have the same intrinsic near-in
frared spectra as quasars, our multiwavelength images allow us to limit any
possible shift to less than 0.3 mag.