[en] Variations of eclipse arrival times have recently been detected in several post-common envelope binaries consisting of a white dwarf and a main-sequence companion star. The generally favored explanation for these timing variations is the gravitational pull of one or more circumbinary substellar objects periodically moving the center of mass of the host binary. Using the new extreme-AO instrument SPHERE, we image the prototype eclipsing post-common envelope binary V471 Tau in search of the brown dwarf that is believed to be responsible for variations in its eclipse arrival times. We report that an unprecedented contrast of $\mathrm{\Delta <!--\; ??\; -->}{m}_H=12.1$ at a separation of 260 mas was achieved, but resulted in a non-detection. This implies that there is no brown dwarf present in the system unless it is 3 mag fainter than predicted by evolutionary track models, and provides damaging evidence against the circumbinary interpretation of eclipse timing variations. In the case of V471 Tau, a more consistent explanation is offered with the Applegate mechanism, in which these variations are prescribed to changes in the quadrupole moment within the main-sequence star.