We study large-scale winds driven from uniformly bright self-gravitating discs radiating near the Eddington limit. We show that the ratio of the radiation pressure force to the gravitational force increases with height above the disc surface to a maximum of twice the value of the ratio at the disc surface. Thus, uniformly bright self-gravitating discs radiating at the Eddington limit are fundamentally unstable to driving large-scale winds. These results contrast with the spherically symmetric case, where super-Eddington luminosities are required for wind formation. We apply this theory to galactic winds from rapidly star-forming galaxies that approach the Eddington limit for dust. For hydrodynamically coupled gas and dust, we find that the asymptotic velocity of the wind is v∞≃ 1.5 vrot and that v∞∝ SFR0.36, where vrot is the disc rotation velocity and SFR is the star formation rate, both of which are in agreement with observations. However, these results of the model neglect the gravitational potential of the surrounding dark matter halo and a (potentially massive) old passive stellar bulge or an extended disc, which act to decrease v∞. A more realistic treatment shows that the flow can either be unbound or bound, forming a ‘fountain flow’ with a typical turning time-scale of tturn∼ 0.1–1 Gyr, depending on the ratio of the mass and radius of the rapidly star-forming galactic disc relative to the total mass and break (or scale) radius of the dark matter halo or bulge. We provide quantitative criteria and scaling relations for assessing whether or not a rapidly star-forming galaxy of given properties can drive unbound flows via the mechanism described in this paper. Importantly, we note that because tturn is longer than the star formation time-scale (gas mass/star formation rate) in the rapidly star-forming galaxies and ultraluminous infrared galaxies for which our theory is most applicable, if rapidly star-forming galaxies are selected as such, they may be observed to have strong outflows along the line of sight with a maximum velocity vmax comparable to ∼1.5 vrot, even though their winds are eventually bound on large scales.