Supermassive black holes (SMBHs) are believed to reside at the centre of massive galaxies such as brightest cluster galaxies (BCGs), the most massive galaxies which can be found in today's Universe. However, as BCGs experienced numerous galaxy mergers throughout their history, the central BH can be significantly kicked from the central region by these dynamical encounters. By combining the Illustris-TNG300 simulations and orbital integration methods, we demonstrate that mergers with satellite galaxies on radial orbits are a main driver for such BH displacements in BCGs. BHs can get ejected to distances varying between a few parsecs to hundreds of kiloparsecs. Our results clearly establish that SMBH offsets are common in BCGs and more precisely a third of our BHs are off-centred at z = 0. This orbital offset can be sustained for up to at least 6 Gyr between z = 2 and z = 0 in half of our BCGs. Since the dense gas reservoirs are located in the central region of galaxies, we argue that the consequences of off-center SMBHs in BCGs are to quench any BH growth and BH feedback.