The LBDS Hercules sample of mJy radio sources at 1.4 GHz - II. Redshift distribution, radio luminosity function, and the high-redshift cut-off

{Abridged} A combination of spectroscopy and broadband photometric redshifts has been used to find the complete redshift distribution of the Hercules sample of millijansky radio sources. These data have been used to examine the evolution of the radio luminosity function (RLF) and its high-redshift cut-off. New redshifts have been measured for eleven sources, and a further ten upper limits are given. The total number of sources with known redshifts in the sample is now 47 (65%). We calculated broadband photometric redshifts for the remaining one-third of the sample. For the luminosity range probed by the present study (P_1.4 > 10^24.5 W/Hz/sr), we use the V/V_max test to show conclusively that there is a deficit of high-redshift (z > 2-2.5) objects. Comparison with the model RLFs of Dunlop & Peacock (1990) shows that our data can now exclude pure luminosity evolution. Two of the models of DP90, and the RLF deduced by direct binning of the data, both favour a luminosity dependence for the high-redshift cut-off, with lower-luminosity sources (P_1.4 \simeq 10^24 W/Hz/sr) in decline by z \simeq 1-1.5 while higher-luminosity sources (P_1.4 \simeq 10^{25-26} W/Hz/sr) decline in comoving number density beyond z \simeq 2-2.5.