We present an extended analysis of the Submillimetre Common User Bolometer Array (SCUBA) observations of the Hubble Deep Field (HDF), expanding the areal coverage of the Hughes et al. study by a factor of 1.8 and containing at least three further sources in addition to the five in that study. We also announce the public release of the reduced data products. The map is the deepest ever made in the submillimetre (submm), obtained in excellent conditions (median 850-mum optical depth of 0.16). Two independent reductions were made, one with SURF and the other with a wholly algorithmic IDL analysis which we present in detail here. Of the three new sources, all appear to be at z greater than or similar to 0.9 and one is provisionally associated with an extremely red object (I - K > 5). There appears to be no significant cross-correlation signal between the 850-mum fluctuations and sources detected by ISOCAM, the Very Large Array (VLA) or Chandra, nor with very red objects (I - K > 4), nor quasars and quasar candidates in the HDF (notwithstanding a small number of individual weak candidate detections). This is consistent with interpretations where the 850-mum selected galaxies are at higher redshifts than those currently probed by ISOCAM/VLA, and predominantly not Compton-thin active galactic nuclei (AGN). There are only one or two compelling cases for the radio source being the submm source. Nevertheless, most SCUBA-HDF point sources have a nearby radio source apparently well-separated from the submm centroid.