Aims. We investigate the colour-magnitude relation of metal-poor globular clusters, the so-called blue tilt, in the Hydra and Centaurus galaxy clusters and constrain the primordial conditions for star cluster self-enrichment. Methods. We analyse U, I photometry for about 2500 globular clusters in the central regions of Hydra and Centaurus, based on VLT/FORS1 data. We measure the relation between mean colour and luminosity for the blue and red subpopulation of the globular cluster samples. We convert these relations into mass-metallicity space and compare the obtained GC mass-metallicity relation with predictions from the star cluster self-enrichment model by Bailin & Harris (2009, ApJ, 695, 1082. For this we include effects of dynamical and stellar evolution and a physically well motivated primordial mass-radius scaling. Results. We obtain a mass-metallicity scaling of Z ∝ M 0.27 ± 0.05 for Centaurus GCs and Z ∝ M 0.40 ± 0.06 for Hydra GCs, consistent with the range of observed relations in other environments. We find that the GC mass-metallicity relation already sets in at present-day masses of a few 10 5 M and is well established in the luminosity range of massive MW clusters like ω Centauri. The inclusion of a primordial mass-radius scaling of star clusters significantly improves the fit of the self-enrichment model to the data. The selfenrichment model accurately reproduces the observed relations for average primordial half-light radii r h ∼ 1−1.5 pc, star formation efficiencies f ∼ 0.3−0.4, and pre-enrichment levels of [Fe/H] − 1.7 dex. The slightly steeper blue tilt for Hydra can be explained either by a ∼30% smaller average r h at fixed f ∼ 0.3, or analogously by a ∼20% smaller f at fixed r h ∼ 1.5 pc. Within the selfenrichment scenario, the observed blue tilt implies a correlation between GC mass and width of the stellar metallicity distribution. We find that this implied correlation matches the trend of width with GC mass measured in Galactic GCs, including extreme cases like ω Centauri and M 54. Conclusions. First, we found that a primordial star cluster mass-radius relation provides a significant improvement to the selfenrichment model fits. Second we show that broadened metallicity distributions as found in some massive MW globular clusters may have arisen naturally from self-enrichment processes, without the need of a dwarf galaxy progenitor.