Using Ly alpha line profiles generated from a grid of M dwarf model atmospheres we calculate the attenuation factor [i.e. Ly alpha (obs)/ Ly alpha (intrin)] due to the interstellar medium as a function of hydrogen column density. Then using selected model atmospheres, attenuation factors were calculated for those M dwarfs with available Ly alpha observations. The prime motivation in this work has been to look afresh at the intrinsic Ly alpha to H alpha flux ratio, an important constraint in the radiative transfer modelling of M dwarfs. For those active dMe stars where both lines were observed, the intrinsic ratio is ~3-5 (with ~50% variation). The major uncertainty in this work has been the interstellar hydrogen column density, emphasizing the need for further work in this area and in particular an accurate model of its variation in all directions.