The impact of metallicity on the mass-loss rate from red giant branch (RGB) stars is studied through its effect on the parameters of horizontal branch (HB) stars. The scaling factors from Reimers (1975) and Schröder & Cuntz (2005) are used to measure the efficiency of RGB mass loss for typical stars in 56 well-studied Galactic globular clusters (GCs). The median values among clusters are, respectively, η R = 0.477 ± 0.070 +0.050 −0.062 and η SC = 0.172 ± 0.024 +0.018 −0.023 (standard deviation and systematic uncertainties, respectively). Over a factor of 200 in iron abundance, η varies by < ∼ 30 per cent, thus mass-loss mechanisms on the RGB have very little metallicity dependence. Any remaining dependence is within the current systematic uncertainties on cluster ages and evolution models. The low standard deviation of η among clusters (≈14 per cent) contrasts with the variety of HB morphologies. Since η incorporates cluster age, this suggests that age accounts for the majority of the "second parameter problem", and that a Reimers-like law provides a good mass-loss model. The remaining spread in η correlates with cluster mass and density, suggesting helium enrichment provides the third parameter explaining HB morphology of GCs. We close by discussing asymptotic giant branch (AGB) mass loss, finding the AGB tip luminosity is better reproduced and η has less metallicity dependence if globular clusters are more co-eval than generally thought.terised by a scaling factor, η, which determines the constant of proportionality in these scaling laws.Calibrating η is important in understanding the post-RGB stages of low-mass stellar evolution, particularly if η varies with other stellar parameters, such as stellar metallicity. No direct variation of metallicity is included in the Reimers and SC05 relations, however metallicity indirectly affects the parameterised mass-loss rate through the consequent variation of stellar radius and the speed at which the star evolves. Mass loss from RGB stars is thought to occur via (magneto-)acoustic processes, hence it should be largely independent of metallicity. If a parameterisation like those of Reimers (1975) and SC05 provides is an accurate representation of the mass-loss rates of RGB stars, we can expect η to be independent of metallicity too.RGB mass loss is notoriously difficult to measure, relying mainly on three tracers. Blueshifted components in optical and near-IR lines trace mass motions close to the stellar surface, but this does not necessarily translate into the rate at which mass is ejected from the star (e.g. McDonald & van Loon 2007; Mészáros et al. 2009). Submm CO line strengths trace material far from the star, but c 9999 RAS 1 The unpublished documentation for this edition can be found at http://arxiv.org/abs/1012.3224. c 9999 RAS, MNRAS 000, 1-22