We have mapped the submillimetre wavelength continuum emission from the Subaru Deep Field (SDF) at 450 and 850 microns with the Submillimetre Common-User Bolometer Array (SCUBA) detector on the James Clerk Maxwell Telescope (JCMT). The near-IR image of the SDF is one of the deepest near-IR images available and contains four `hyper extremely red objects (HEROs). These data allow us to test the connection between `extremely red objects (EROs) found in IR surveys and the population of bright submillimetre sources found with SCUBA. We present a weak measurement of the average flux of the four K-band selected HEROs of 1.15 (+/-0.46) mJy, which fails to support the hypothesis that HEROs should be bright SCUBA sources. Our data are consistent with the HEROs being objects with SEDs like that of Arp220 out to z~1.7, however, the extinction in the HEROs must be about 1 magnitude greater in the J-band than is the case for Arp220 and they would need to be 1.7 times as luminous as Arp220. On the other hand, an evolutionary model of elliptical galaxies at z~2-3 in a dusty starburst phase is also in agreement with the submillimetre data, as was originally proposed for the HEROs.