We present results from an optical four-colour (BVRI) CCD imaging study of a hard X-ray flux-limited sample of AGN, which are mainly Seyfert 1s. This work complements our near-infrared study of the same sample (Papers I and II). The contribution to the nuclear flux from the underlying galaxy is estimated by deconvolving the radial luminosity profiles into an unresolved nuclear component, and bulge and disc components. We find that starlight contributes a significant fraction of the nuclear light even in a small aperture for most of the Seyferts. Lower luminosity nuclei have a higher fraction of their nuclear emission from the underlying galaxy. This correlation is tighter than was found at the near-infrared wavelengths, probably a result of the higher accuracy of the deconvolution process at optical wavelengths compared to that achieved using the near-infrared images. The peak of the fractional stellar contribution occurs at wavelengths covered by the I filter (about 8000 angstrom). On the other hand, the absolute energy distribution of the stellar component peaks at wavelengths covered by the H band (centred at 1.6 mum), as does the energy distribution of a normal galaxy. There is a single peak in the stellar fraction versus wavelength distribution, which decreases smoothly towards the blue and towards the infrared. We look for a correlation between the calcium triplet absorption strength and the stellar fraction in the I band, but we cannot discriminate between the calcium absorption arising in the underlying galaxy or in a nuclear cluster of red supergiants.