The growth of epitaxial Co layers on Fe(001) by simultaneous thermal evaporation of Co atoms and ion bombardment with low-energy (300-1000 eV) Ar ions has been investigated for a wide range of ion/atom flux ratios (up to 0.5) and compared with growth by a purely thermal deposition procedure. Co nominal thickness was in the 2-50 monolayer (ML) range. At low Co nominal thickness (2-10 monolayers), the thermally grown films tend to form islands, while the ion beam-assisted growth results in the formation of a continuous Co layer. Structural characterisation of the Co layer was performed by exploiting the dependence of the Auger emission intensity on the angle of incidence of the primary exciting electron beam (primary-beam diffraction modulated electron emission, PDMEE). For purely thermal deposition, transition from the cubic phase to the equilibrium h.c.p. phase occurs at a critical nominal thickness of 15 ML, both structures showing a significant strain (4% contraction and 6% expansion compared to the ideal b.c.c. and h.c.p. phases, respectively). Ion assistance has proved to be effective in lowering both the critical thickness of the cubic phase and strain in the hexagonal Co film. The relevant parameter which comes into play in determining the effectiveness of ion assistance has been found to be the average energy deposited per atom.