A combination of ground-based (NTT and VLT) and Hubble Space Telescope (HST) (HDF–N and HDF–S) public imaging surveys has been used to collect a sample of 1712 I-selected and 319 K≤21 galaxies observed with an extended spectral coverage from U to K bands. Photometric redshifts have been obtained for all these galaxies, using a spectral library computed from Bruzual & Charlot models. The results have been compared with the prediction of an analytic rendition of the current cold dark matter (CDM) hierarchical models for galaxy formation that explicitly accounts for magnitude limits and dust extinction. We focus in particular on two observed quantities: the galaxy redshift distribution at K≤21 and the evolution of the UV luminosity density. The former has been proposed by Kauffmann & Charlot to be a very robust prediction of any CDM hierarchical model, and we show that it is remarkably constant among different cosmological models. The derived photometric redshift distribution is in agreement with the hierarchical CDM prediction, with a fraction of only 5 per cent of galaxies detected at z≥2. This result strongly supports hierarchical scenarios where present-day massive galaxies are the result of merging processes. The observed UV luminosity density in our I-selected sample is confined within a factor of 4 over the whole range 0<z<4.5, in agreement with previous spectroscopic and photometric surveys. CDM models in a critical ( Ω=1, Λ=0) Universe are not able to produce the density of UV photons that is observed at z≥3. CDM models in a Λ-dominated universe are in better agreement at 3≤z≤4.5, but predict a pronounced peak at z≃1.5 and a drop by a factor of 8 from z=1.5 to z=4 that is not observed in the data. We conclude that improvements are required in the treatment of the physical processes directly related to the star formation rate (SFR), e.g. the starburst activity in merger processes and/or different recipes for linking the supernova feedback to the star formation activity.