  We present the first near-infrared (K'-band) homogeneous observations of a
complete sub-sample of the 3CR radio catalogue comprising all High Excitation
Galaxies (HEGs) at z<0.3. After showing that the surface brightness
decomposition technique to measure central point-like sources is affected by
significant uncertainties for the objects in the studied sample, we present a
new, more accurate method based on the R-K' color profile. Via this method we
find a substantial nuclear K'-band excess in all but two HEGs -- most likely
directly associated to their nuclear emission -- and we measure the
corresponding 2.12 $\mu$m nuclear luminosities. Within the frame of the
unification scheme for radio-loud active galactic nuclei, it appears that
obscuration alone is not able to account for the different nuclear properties
of the majority of the HEGs and Broad Line Radio Galaxies (BLRGs), and also
scattering of the (optically) hidden nuclear light from a compact region must
be invoked. More precisely, for ~70% of the HEGs the observed point-like
optical emission is dominated by the scattered component, while in the K'-band
both scattered and direct light passing through the torus contribute to the
observed nuclear luminosity. The estimated fraction of scattered light ranges
from a few tenths to a few percent, while the torus extinction is between
15<A_{V,torus}<50 mag with only a few exceptions with lower obscuration.
