We present wide-field Keck telescope imaging of the globular cluster (GC) systems around NGC 1407 and 1400 in the Eridanus galaxy cloud. This is complemented by Hubble Space Telescope (HST) images from the Advanced Camera for Surveys of NGC 1407 and Wide Field and Planetary Camera 2 images of NGC 1400. We clearly detect bimodality in the GC colour distribution of NGC 1407. The blue GC subpopulation has a mean colour of B - I = 1.61 and a relative contribution of around 40 per cent, whereas the red subpopulation with B - I = 2.06 contributes 60 per cent to the overall GC system. Assuming old ages, this corresponds to [Fe/H] = -1.45 and -0.19. Both subpopulations are intrinsically broad in colour (indicating a range in ages and/or metallicities), with the red subpopulation being broader than the blue. The GC colour distribution for NGC 1400 is less clear cut than for NGC 1407, however, we also find evidence for a bimodal distribution. We find the NGC 1407 red GCs to be 20 per cent smaller in size than the blue ones. This is consistent with the expectations of mass segregation in an old coeval GC system. Half a dozen large objects (20-40 pc), with GC-like colours are identified, which are probably background galaxies. The HST data sets allow us to probe to small galactocentric radii. Here we find both GC systems to possess a GC surface density distribution which is largely constant in these inner galaxy regions. We fit isothermal-like profiles and derive GC system core radii of 9.4 kpc for NGC 1407 and 5.8 kpc for NGC 1400. For NGC 1407 we are able to separate the surface density distribution into blue and red subpopulations, giving 17.8 and 7.6 kpc, respectively. Outside this central region, the radial profile of the GC surface density is similar to that of the galaxy light for NGC 1407 but it is flatter for NGC 1400. The mean GC magnitude appears to be constant with galactocentric radius. We find that for both galaxies, the GC systems have a similar ellipticity and azimuthal distribution as the underlying galaxy starlight. A fit to the GC luminosity function gives a distance modulus of 31.6, which is in good agreement with distances based on the Faber-Jackson relation and the Virgo infall corrected velocity.