We investigate where brightest cluster galaxies (BCGs) sit on the Fundamental Plane of black hole (BH) activity, an established relation between the X-ray luminosity, the radio luminosity and the mass of a BH. Our sample mostly consists of BCGs that lie at the centres of massive, strong cooling flow clusters, therefore requiring extreme mechanical feedback from their central active galactic nucleus (AGN) to offset cooling of the intracluster plasma (Lmech>1044 -1045 erg s−1). Based on the BH masses derived from the and MBH - MK correlations, we find that all of our objects are offset from the plane such that they appear to be less massive than predicted from their X-ray and radio luminosities (to more than a 99 per cent confidence level). For these objects to be consistent with the Fundamental Plane, the and MBH - MK correlations therefore seem to underestimate the BH masses of BCGs, on average by a factor of 10. Our results suggest that the standard relationships between BH mass and host galaxy properties no longer hold for these extreme galaxies. Furthermore, our results imply that if these BHs follow the Fundamental Plane, then many of those that lie in massive, strong cool core clusters must be ultramassive with MBH > 1010 M⊙. This rivals the largest BH masses known and has important ramifications for our understanding of the formation and evolution of BHs.