We have studied the submillimetre ( submm) properties of the following classes of near- infraredselected ( NIR- selected) massive galaxies at high redshifts: BzK- selected star- forming galaxies ( BzKs); distant red galaxies ( DRGs); and extremely red objects ( EROs). We used the SCUBA HAlf Degree Extragalactic Survey ( SHADES), the largest uniform submm survey to date. Partial overlap of SIRIUS/ NIR images and SHADES in Subaru/ XMM - Newton deep field has allowed us to identify four submm- bright NIR- selected galaxies, which are detected in the mid- IR, 24 m, and the radio, 1.4 GHz. We find that all of our submm- bright NIR- selected galaxies satisfy the BzK selection criteria, i. e. BzK = ( z - K) AB - ( B - z) AB >= - 0.2, except for one galaxy whose B - z and z - K colours are however close to the BzK colour boundary. Two of the submm- bright NIR- selected galaxies satisfy all of the selection criteria we considered, i. e. they belong to the BzK - DRG - ERO overlapping population, or ` extremely red' BzKs. Although these extremely red BzKs are rare ( 0.25 arcmin(-2)), up to 20 per cent of this population could be submm galaxies. This fraction is significantly higher than that found for other galaxy populations studied here. Via a stacking analysis, we have detected the 850- mu m flux of submm- faint BzKs and EROs in our SCUBAmaps. While the contribution of z similar to 2 BzKs to the submm background is about 10 - 15 per cent and similar to that from EROs typically at z similar to 1, BzKs have a higher fraction (similar to 30 per cent) of submm flux in resolved sources compared with EROs and submm sources as a whole. From the spectral energy distribution ( SED) fitting analysis for both submm- bright and submm- faint BzKs, we found no clear signature that submm- bright BzKs are experiencing a specifically luminous evolutionary phase, compared with submm- faint BzKs. An alternative explanation might be that submm- bright BzKs are more massive than submm- faint ones.