Space and water heating represent a significant share of the overall energy consumption in the domestic sector. Decarbonising heat, though challenging, is acknowledged as having a key role to play(as exemplifiedby the Domestic Renewable Heat Incentive launched in 2014 in the UK, amongst other)in achievingemissionsreduction targets andalleviatingproblems related to energy shortage and environmental deterioration. Novel, highly efficientheating technologies have attracted increasing interest in this context, in particular in regions with colderclimatesand higherheating demands. Specifically, thermally-driven heat-pumping technologies are a promising solution to meetingenergy-efficiency targets by increasing the effectiveheat-to-fuelratio(HFR)of heatingsystems. In this paper,thermally-driven integrated organic Rankine cycle (ORC) and heat pump (HP) systems are proposed for domestic heating applications, in which the ORC system is driven by heat from fuel (e.g., gas) combustion and generates power to drive an air-source vapour-compression HP system. A heat-transfer fluid is heatedin the condensers of the two sub-systems to the required temperature for heat provision. Two system configurations with reversed heat-transfer fluidflow directions are presented and compared. Suitable, lowglobal-warming-potential (GWP) working fluids for both the ORC and HP systems are considered and parametric optimisation is performed to determine optimal thermodynamic performanceand system layouts. In aconfiguration in whichthe heat-transfer fluidflows firstthroughthe HP condenser andthen through the ORC condenser in series,the HFRreaches values of 1.26-2.04 forair-source temperaturesranging from -15 to 15 °C and for heat provision temperaturesfrom 35 °C to 60 °C.Aperformance enhancement up to 8-19% relative to theconfiguration withthe heat-transfer fluidflowingin thereversedirection, i.e., through the ORC condenser and then theHP condenser in series, can be achieved. The specific investment costsof both configurations under typical conditions are around 600 £/kWth, which indicates that the proposed systems are slightly higher but still economically competitive with existing HPproducts available on the market,thus demonstrating the potential of exploiting such novel systems for domestic heating in practical applications.