We have used maximum entropy eclipse mapping to recover images of the visual surface brightness distribution of the primary component of the RS CVn eclipsing binary SV Cam, using high-precision photometry data obtained during three primary eclipses with STIS aboard the Hubble Space Telescope. These were augmented by contemporaneous ground-based photometry secured around the rest of the orbit. The goal of these observations was to determine the filling factor and size distribution of starspots too small to be resolved by Doppler imaging. The information content of the final image and the fit to the data were optimised with respect to various system parameters using the chi^2 landscape method, using an eclipse mapping code that solves for large-scale spot coverage. It is only with the unprecedented photometric precision of the HST data (0.00015 mag) that it is possible to see strong discontinuities at the four contact points in the residuals of the fit to the lightcurve. These features can only be removed from the residual lightcurve by the reduction of the photospheric temperature, to synthesise high unresolvable spot coverage, and the inclusion of a polar spot. We show that this spottedness of the stellar surface can have a significant impact on the determination of the stellar binary parameters and the fit to the lightcurve by reducing the secondary radius from 0.794 +/- 0.009 Rsun to 0.727 +/- 0.009 Rsun. This new technique can also be applied to other binary systems with high precision spectrophotometric observations.