We report a method for the growth of carbon nanotubes on carbon fibre using a low temperature growth technique which is infused using a standard industrial process, to create a fuzzy fibre composite with enhanced electrical characteristics. Conductivity tests reveal improvements of 510% in the out-of-plane and 330% in the in-plane direction for the nanocomposite compared to the reference composite. Further analysis of current-voltage (I-V) curves confirm a transformation in the electron transport mechanism from charge - hopping in the conventional material, to an Ohmic diffusive mechanism for the carbon nanotube modified composite. Single fibre tensile tests reveal a tensile performance decrease of only 9.7% after subjecting it to our low temperature carbon nanotube growth process, which is significantly smaller than previous reports. Our low-temperature growth process uses substrate water-cooling to maintain the bulk of the fibre material at lower temperatures, whilst the catalyst on the surface of the carbon fibre is at optimally higher temperatures required for carbon nanotube growth. The process is large-area production compatible with bulk-manufacturing of carbon fibre polymer composites.