We present an end-to-end description of the formation of globular clusters (GCs) combining a treatment for their formation and dynamical evolution within galaxy haloes with a state-of-the-art semi-analytic simulation of galaxy formation. Our approach allows us to obtain exquisite statistics to study the effect of the environment and assembly history of galaxies, while still allowing a very efficient exploration of the parameter space. Our reference model, including both efficient cluster disruption during galaxy mergers and dynamical friction of GCs within the galactic potential, accurately reproduces the observed correlation between the total mass in GCs and the parent halo mass. A deviation from linearity is predicted at low-halo masses, which is driven by a strong dependence on morphological type: bulge-dominated galaxies tend to host larger masses of GCs than their later-type counterparts. While the significance of the difference might be affected by resolution at the lowest halo masses considered, this is a robust prediction of our model and a natural consequence of the assumption that cluster migration into the halo is triggered by galaxy mergers. Our model requires an environmental dependence of GC radii to reproduce the observed low-mass mass distribution of GCs in our Galaxy. At GC masses >10(6)M(circle dot), our model predicts fewer GCs than observed, due to an overly aggressive treatment of dynamical friction. Our model reproduces well the metallicity distribution measured for Galactic GCs, even though we predict systematically younger GCs than observed. We argue that this adds further evidence for an anomalously early formation of the stars in our Galaxy.