We explore the implications for the high redshift universe of ``state-of-the-art models for the chemical and spectrophotometric evolution of spiral galaxies. The models are based on simple ``scaling relations for discs, obtained in the framework of Cold Dark Matter models for galaxy formation, and were ``calibrated as to reproduce the properties of the Milky Way and of nearby discs (at redshift z~0). In this paper, we compare the predictions of our ``hybrid approach to galaxy evolution to observations at moderate and high redshift. We find that the models are in fairly good agreement with observations up to z~1, while some problems appear at higher redshift (provided there is no selection bias in the data); these discrepancies may suggest that galaxy mergers (not considered in this work) played a non negligible role at z>1. We also predict the existence of a ``universal correlation between abundance gradients and disc scalelengths, independent of redshift.