Low temperature carbonisation (500 degrees C) of poly-acrylonitrile nanofibres (typically 100 nm diameter) electrospun into a nanoweb-like deposit on tin-doped indium oxide (ITO) substrates (or as free-standing membrane over glass capillaries) yields active carbon film electrodes but with only relatively low electrochemical activity. Without resorting to higher carbonisation temperatures, substantial improvements in both electrical conductivity and electron transfer reactivity are observed after "surface-graphenisation", that is coating with graphene-oxide prior to vacuum carbonisation. Improvements in voltammetric characteristics are demonstrated for both membranes mounted on ITO substrates and free-standing membranes suspended over the end of a borosilicate glass capillaries for (i) the aqueous phase hydroquinone/benzoquinone redox system and (ii) the biphasic oil jaqueous ion transfer redox system tetraphenylpor-phyrinato-Mn(III/II) in 4-phenyl-(3-propyl)-pyridine).