Metcalfe et al. (1995, 1996) have shown that galaxy counts from the UV to the near-IR are well-fitted by simple evolutionary models where the space density of galaxies remains constant with look-back time while the star-formation rate rises exponentially. We now extend these results, first by using data from the Herschel Deep Field to show that these same models give detailed fits to the faint galaxy r - i : b - r colour-colour diagram. We then use these models to predict the number counts of high redshift galaxies detected by the Lyman break technique. At z ≈ 3 there is almost exact agreement between our prediction and the data, suggesting that the space density of galaxies at z ≈ 3 may be close to its local value. At z ≈ 4 the space density of bright galaxies remains unchanged; however, the space density of dwarf galaxies is significantly lower than it is locally, suggesting that we have detected an epoch of dwarf galaxy formation at z ≈ 4. Finally, significant numbers of Lyman-break galaxy candidates are also detected at z ≈ 6 in the Hubble and Herschel Deep Fields; taking this observation together with a number of recent detections of spectroscopically confirmed z ≈ 6 galaxies suggests that the space density of bright galaxies at z ≈ 6 remains comparable to the local space density, and thus that the epoch of formation of bright galaxies may lie at yet higher redshift.