Millimetre wave corrugated waveguide-horn structures are used as both single-moded and multi-moded bolometer feeds in a number of cosmic microwave background (CMB) experiments (e.g. PLANCK, Archeops, QUaD). Such horns tend to be employed over a relatively wide bandwidth and for single-moded horns the waveguide acts as the high pass filter. In this paper we report on our investigation on how the waveguide details determine the exact location of the low frequencyband edge of such corrugated horns. A sharp step-like band edge, below which there is negligible propagation, is ideallyrequired. Furthermore anyleakage below the expected cut-off, possible in corrugated guides, could lead to non-idealised cross-polar effects. Typically deeper corrugations are required in the waveguide filter than at the horn aperture for wide bandwidth operation, thus necessitating a transition section over which the corrugation depth smoothlyvaries. An electromagnetic mode matching technique and a surface impedance hybrid mode model are used to compute the horn transmission characteristics. We have also undertaken laboratorymeasurements of the band edge of prototype corrugated horns in order to test the models.