X-ray reverberation, where light-travel time delays map out the compact geometry around the inner accretion flow in supermassive black holes, has been discovered in several of the brightest, most variable and well-known Seyfert galaxies. In this work, we expand the study of X-ray reverberation to all Seyfert galaxies in the XMM–Newton archive above a nominal rms variability and exposure level (a total of 43 sources). Approximately 50 per cent of sources exhibit iron K reverberation, in that the broad iron K emission line responds to rapid variability in the continuum. We also find that on long time-scales, the hard band emission lags behind the soft band emission in 85 per cent of sources. This ‘low-frequency hard lag’ is likely associated with the coronal emission, and so this result suggests that most sources with X-ray variability show intrinsic variability from the nuclear region. We update the known iron K lag amplitude versus black hole mass relation, and find evidence that the height or extent of the coronal source (as inferred by the reverberation time delay) increases with mass accretion rate.