We report electrical conductivity measurements of polymethyl-methacrylate filled by onion-like carbon particles with a primary particle size of approximate to 5 nm. We show that the conductivity sigma is exceptionally high even at very low loadings and that its low-temperature dependence follows a Coulomb gap regime at atmospheric pressure and an activated behavior at a pressure of 2 GPa. We interpret this finding in terms of the enhancement under the applied pressure of the effective dielectric permittivity within the aggregates of onion-like carbons, which improves the screening of the Coulomb interaction and reduces the optimal hopping distance of the electrons. Published under license by AIP Publishing.