The low concentration behaviour and the increase of the dielectric constant in carbon nanotubes/polymer nanocomposites near the percolation threshold are still not well understood. In this work, a numerical model has been developed which focuses on the effect of the inclusion of conductive fillers in a dielectric polymer matrix on the dielectric constant and the dielectric strength. Experiments have been carried out in carbon nanotubes/poly(vinylidene fluoride) nanocomposites in order to compare to the simulation results. This work shows how the critical concentration is related to the formation of capacitor networks and that these networks give rise to high variations in the electrical properties of the composites. Based on numerical studies, the dependence of the percolation transition on the preparation of the nanocomposite is discussed. Finally, based on numerical and experimental results, both ours and from other authors, the causes of anomalous percolation behaviour of the dielectric constant are identified.