In this paper, we investigate the eclipse timing of the polar binary HU?Aquarii that has been observed for almost two decades. Recently, Qian et al. attributed large (OC) deviations between the eclipse ephemeris and observations to a compact system of two massive Jovian companions. We improve the Keplerian, kinematic model of the light travel time effect and re-analyse the whole currently available data set. We add almost 60 new, yet unpublished, mostly precision light curves obtained using the time high-resolution photopolarimeter Optical Timing Analyzer (OPTIMA), as well as photometric observations performed at the Monitoring Network of Telescopes/North, Physics Innovations Robotic Astronomical Telescope Explorer and Carlos Sanchez Telescope. We determine new mid-egress times with a mean uncertainty at the level of 1?s or better. We claim that because the observations that currently exist in the literature are non-homogeneous with respect to spectral windows (ultraviolet, X-ray, visual and polarimetric mode) and the reported mid-egress measurements errors, they may introduce systematics that affect orbital fits. Indeed, we find that the published data, when taken literally, cannot be explained by any unique solution. Many qualitatively different and best-fit two-planet configurations, including self-consistent, Newtonian N-body solutions may be able to explain the data. However, using high-resolution, precision OPTIMA light curves, we find that the (OC) deviations are best explained by the presence of a single circumbinary companion orbiting at a distance of similar to 4.5?au with a small eccentricity and having similar to 7 Jupiter masses. This object could be the next circumbinary planet detected from the ground, similar to the announced companions around close binaries HW?Vir, NN?Ser, UZ?For, DP?Leo, FS?Aur or SZ?Her, and planets of this type around Kepler-16, Kepler-34 and Kepler-35.