A means of enhancing electrical and thermal conductivities of carbon fibre reinforced polymer (CFRP) composites is investigated for the purpose of reducing damage when electric current and/or heat is introduced into a CFRP structure. The addition of commercially available graphene oxide (GO) nano-flakes dispersed into an epoxy resin is studied; quantities up to 6.3 vol% are used in a vacuum infusion process with carbon fibre fabric to form CFRP laminates. Measurements of the anisotropic electrical and thermal conductivity of the laminate were conducted on CFRP specimens with and without the GO nano-flakes. It is shown that the electrical conductivity in the through-thickness direction increased markedly, reaching values up to 0.18 S/cm, when 6.3 vol% of GO was added into the epoxy, showing a threefold increase compared to the neat CFRP. Similar improvement was also found in the thermal through-thickness conductivity for the same filler content, where the laminate exhibited identical values in both transverse and through-thickness directions. However, the properties transverse to the fibres were not greatly affected by the GO addition. To assess the effect of the GO on the mechanical properties, interlaminar shear strength tests were conducted that showed that the addition of the GO significantly enhanced the through-thickness shear strength.