Structural supercapacitors are multifunctional devices able to bear mechanical load while storing electrical energy. Carbon fibres can be used as a bifunctional component within structural supercapacitors, acting both as current collector and mechanical reinforcement. A promising route to such devices is to increase the surface area of carbon fibres, which can be achieved by the deposition of active materials, and embed them into a structural electrolyte. A highly sulfonated, high porosity hypercrosslinked polymer was deposited onto carbon fibres by electrophoretic deposition from an aqueous suspension. We investigated the effect of polymer and binder concentration in the deposition suspension on the electrochemical properties of the coated carbon fibre electrodes. Multifunctional structural composite supercapacitors had a fibre volume fraction of only 21% and possessed a tensile strength and Young's modulus of 495 MPa and 49 GPa, respectively. A specific capacitance of 1.2 F/g was reached, comparable to graphene coated carbon fibre electrodes. At room temperature and ambient humidity an energy density of 39 mWh/kg and a power density of 15 W/kg were measured. We demonstrate that moisture plays a major role in the energy storage mechanism in these SCs.