© 2016 The Authors. Published by Oxford University Press on behalf of The Royal Astronomical Society. We examine the HI-based star formation efficiency (SFEHI), the ratio of star formation rate to the atomic hydrogen (H I) mass, in the context of a constant stability star-forming disc model. Our observations of HI-selected galaxies show SFEHI to be fairly constant (log SFEHI = -9.65 yr-1 with a dispersion of 0.3 dex) across ~5 orders of magnitude in stellar masses. We present a model to account for this result, whose main principle is that the gas within galaxies forms a uniform stability disc and that stars form within the molecular gas in this disc. We test two versions of the model differing in the prescription that determines the molecular gas fraction, based on either the hydrostatic pressure or the stellar surface density of the disc. For high-mass galaxies such as the Milky Way, we find that either prescription predicts SFEHI similar to the observations. However, the hydrostatic pressure prescription is a more accurate SFEHI predictor for low-mass galaxies. Our model is the first model that links the uniform SFEHI observed in galaxies at low redshifts to star-forming discs with constant marginal stability. While the rotational amplitude Vmax is the primary driver of disc structure in our model, we find that the specific angular momentum of the galaxy may play a role in explaining a weak correlation between SFEHI and effective surface brightness of the disc.