Domestic heating has a large share in the UK total energy consumption and significant contribution to the greenhouse gas emissions since it is mainly fulfilled by fossil fuels. Therefore, decarbonising the heating system is essential and an option to achieve this is by heating system electrification through heat pumps (HP) installation in combination with renewable power generation. A potential increase in performance and flexibility can be achieved by pairing HP with thermal energy storage (TES), which allows the shifting of heat demand to off peak periods or periods with surplus renewable electricity. We present a design and operational optimisation model which is able to assess the performance of HP–TES relative to conventional heating systems. The optimisation is performed on a synthetic heat demand model which requires only the annual heat demand, temperature and occupancy profiles. The results show that the equipment and operational cost of a HP system without TES are significantly higher than for a conventional system. However, the integration of TES and time-of-use tariffs reduce the operational cost of the HP systems and in combination with the Renewable Heating Incentive make the HP systems cost competitive with conventional systems. The presented demand model and optimisation procedure will enable the design of low carbon district heating systems which integrate the heating system with the variable renewable electricity supply.