We report scanning Kerr microscopy observations of a fine-scale (1-5 mu m) magnetic domain structure in epitaxial Fe/GaAs(001) thin films. This fine-scale domain structure develops only during the magnetisation reversal process with fields applied very close (<1 degrees) to the hard anisotropy axis and results from sub-micron-scale inhomogeneities in the film structure. We show that this fine-scale domain structure is responsible for the previously reported collapse (Daboo et al., Phys. Rev, B, 22 (1995) 15964) of the hysteresis leaps probed for the magnetisation component M(perp) perpendicular to the applied field in the plane of the film.