We perform a detailed analysis of thermal leptogenesis in the framework of seesaw models which approximately conserve lepton number. These models are known to allow for large Yukawa couplings and a low seesaw scale in agreement with neutrino mass constraints, and hence to lead to large lepton flavour violating rates that can be probed experimentally. Although large Yukawa couplings lead to (inverse) decay rates much larger than the Hubble expansion rate, we show that the leptogenesis washout induced is generically small if the mass splitting between the right-handed neutrinos is small enough. As a result, large lepton flavour violating rates are compatible with successful leptogenesis. We emphasize that this scenario does not require any particular flavour structure. A small splitting is natural and radiatively stable in this context because it is protected by the lepton number symmetry.