Abstract We present the detection of 89 low surface brightness (LSB), and thus low stellar density galaxy candidates in the Perseus cluster core, of the kind named ‘ultra-diffuse galaxies’, with mean effective V-band surface brightnesses 24.8–27.1 mag arcsec−2, total V-band magnitudes −11.8 to −15.5 mag, and half-light radii 0.7–4.1 kpc. The candidates have been identified in a deep mosaic covering 0.3 deg2, based on wide-field imaging data obtained with the William Herschel Telescope. We find that the LSB galaxy population is depleted in the cluster centre and only very few LSB candidates have half-light radii larger than 3 kpc. This appears consistent with an estimate of their tidal radius, which does not reach beyond the stellar extent even if we assume a high dark matter content (M/L = 100). In fact, three of our candidates seem to be associated with tidal streams, which points to their current disruption. Given that published data on faint LSB candidates in the Coma cluster – with its comparable central density to Perseus – show the same dearth of large objects in the core region, we conclude that these cannot survive the strong tides in the centres of massive clusters.