Galaxy number counts- IV. surveying the Herschel deep field in the near-infrared

(abridged) We present results from two new near-infrared imaging surveys. One covers 47.2 arcmin^2 to K(3\sigma)<20 whilst a second, deeper survey covers a sub-area of 1.8 arcmin^2 to K(3\sigma)<22.75. Over the entire area we have extremely deep UBRI photometry. Our K- counts are consistent with the predictions of non-evolving models with 0 < q0 <0.5. The K-selected (B-K) galaxy colour distributions move sharply bluewards fainter than K~20 and at at brighter magnitudes (K<20) our observed colour distributions indicate a deficiency of red, early-type galaxies at z~1 in comparison with passively evolving models. This implies either a pure luminosity evolution (PLE) model with a low level of continuing star-formation following an an initial burst, or dynamical merging. At fainter magnitudes, the continuing bluewards trend observed in (B-K) can be explained purely in terms of passively evolving PLE models. Our observed numbers of (I-K)>4 galaxies at K<20 exhibit the same deficiency, suggesting that at least part of the larger deficit observed in (B-K) at K<20 may be due to star-formation rather than dynamical merging. Finally, as we and others have noted, the number-redshift distribution at 18<K<19 of recent, deep K- selected redshift surveys is well fitted by non-evolving models; passively evolving models with a Salpeter or Scalo initial mass functions overpredict the numbers of galaxies with z>1. Dynamical merging is one possible solution to reduce the numbers of these galaxies but a dwarf-dominated IMF for early-type galaxies could offer an alternative explanation; we show that this model reproduces both the optical-infrared colour distributions and the K- band galaxy counts.