We present the first near-infrared ( K ^ { \prime } -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 ^ { \prime } color profile . Via this method we find a substantial nuclear K ^ { \prime } -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 \sim 70 % of the HEGs the observed point-like optical emission is dominated by the scattered component , while in the K ^ { \prime } -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 .