We present results from a 54.7 live-day shielded run of the DRIFT-IId detector, the world's most sensitive, directional, dark matter detector. Several improvements were made relative to our previous work including a lower threshold for detection, a more robust analysis and a tenfold improvement in our gamma rejection factor. After analysis, no events remain in our fiducial region leading to an exclusion curve for spin-dependent WIMP-proton interactions which reaches 0.28pb at 100GeV/c2, a fourfold improvement on our previous work. We also present results from a 45.4 live-day unshielded run of the DRIFT-IId detector during which 14 nuclear recoil-like events were observed. We demonstrate that the observed nuclear recoil rate of 0.31 ± 0.08 events per day is consistent with detection of ambient, fast neutrons emanating from the walls of the Boulby Underground Science Facility.