We extended our analytical effective medium theory [ Phys. Rev. B 81 045202 (2010)] to describe the temperature-dependent hopping charge carrier mobility at arbitrary electric fields in the large carrier density regime. Special emphasis was made to analyze the influence of the lateral electric field on the Meyer–Neldel (MN) phenomenon observed when studying the charge mobilities in thin-film organic field-effect transistors (OFET). Our calculations are based on the average hopping transition time approach, generalized for large carrier concentration limit finite fields, and taking into account also spatial energy correlations. The calculated electric field dependences of the hopping mobility at large carrier concentrations are in good agreement with previous computer simulations data. The shift of the MN temperature in an OFET upon applied electric field is shown to be a consequence of the spatial energy correlation in the organic semiconductor film. Our calculations show that the phenomenological Gill equation is clearly inappropriate for describing conventional charge carrier transport at low carrier concentrations. On the other hand a Gill-type behavior has been observed in a temperature range relevant for measurements of the charge carrier mobility in OFET structures. Since the present model is not limited to zero-field mobility, it allows a more accurate evaluation of important material parameters from experimental data measured at a given electric field. In particular, we showed that both the MN and Gill temperature can be used for estimating the width of the density of states distribution.