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 exemplified by the Domestic Renewable Heat Incentive launched in 2014 in the UK, amongst other) in achieving emissions reduction targets and alleviating problems related to energy shortage and environmental deterioration. Novel, highly efficient heating technologies have attracted increasing interest in this context, in particular in regions with colder climates and higher heating demands. Specifically, thermally-driven heat-pumping technologies are a promising solution to meeting energy-efficiency targets by increasing the effective heat-to-fuel ratio (HFR) of heating systems. 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 heattransfer fluid is heated in the condensers of the two sub-systems to the required temperature for heat provision. Two system configurations with reversed heat-transfer fluid flow directions are presented and compared. Suitable, low global-warming-potential (GWP) working fluids for both the ORC and HP systems are considered and parametric optimisation is performed to determine optimal thermodynamic performance and system layouts. In a configuration in which the heat-transfer fluid flows first through the HP condenser and then through the ORC condenser in series, the HFR reaches values of 1.26-2.04 for air-source temperatures ranging from -15 to 15 °C and for heat provision temperatures from 35 °C to 60 °C. A performance enhancement up to 8-19% relative to the configuration with the heat-transfer fluid flowing in the reverse direction, i.e., through the ORC condenser and then the HP condenser in series, can be achieved. The specific investment costs of both configurations under typical conditions are around 600 £/kWth, which indicates that the proposed systems are slightly higher but still economically competitive with existing HP products available on the market, thus demonstrating the potential of exploiting such novel systems for domestic heating in practical applications.