Research is presented aiming to increase both power and energy density of lithium batteries by applying composite cathodes containing sulphur, which has a high theoretical specific capacity of 1675 Ah/kgS and is an abundant and low-cost material, and increase the power density of the cells by creating battery-supercapacitor hybrids with the hybridisation carried out at electrode material level. The focus of current research worldwide has been to increase the cyclability of lithium-sulphur (Li-S) batteries, which has been accomplished by devising composite sulphur cathodes, to avoid cathode degradation due to the expansion of sulphur to accommodate the formation of sulphides, and various functionalisation approaches to trap the sulphides and avoid the 'shuttle' effect during charge. However, the theoretical capacity of sulphur has not been achieved even at first discharge, lowering the expected energy density, and this is further compounded by the fact that only a fraction of the composite cathode is sulphur. Modelling studies have shown that access of all sulphur by the Li+ ions in the micropores is critical and formation of sufficient amounts of higher order sulphides during the first stage of discharge is needed, to be able to obtain a long second stage discharge plateau. The first stage of our study is focused on demonstrating homogeneous and deep sulphur impregnation of porous carbonaceous material to create cathodes with more than 50 wt% sulphur in a supercapacitor-type, porous, host matrix. Repeated discharges are carried out after which we have achieved the theoretical specific capacity of sulphur at first discharge (cumulative curve in Figure 1). We shall continue with parametric studies to investigate the effect of different amounts of sulphur in the composite cathode on the pore size distribution and discharge capacity. The second part of this study includes the investigations into lithium battery-supercapacitor cells hybridised at electrode material level, in combinations of parallel and in series material parts in equivalent circuit models. The effect of the supercapacitor porous carbonaceous electrode materials on the voltage of the cell in galvanostatic charge-discharge curves will be presented in experimental investigations for half-cells of both sides and full cells. Some novel cell architectures will be presented aiming at minimising any detrimental reactions in the supercapacitor materials within the battery cell window.