The interaction between electricity and heat systems will play an important role in facilitating the cost effective transition to a low carbon energy system with high penetration of renewable generation. This paper presents a novel integrated electricity and heat system model in which, for the first time, operation and investment timescales are considered while covering both the local district and national level infrastructures. This model is applied to optimize decarbonization strategies of the U.K. integrated electricity and heat system, while quantifying the benefits of the interactions across the whole multi-energy system and revealing the trade-offs between portfolios of: 1) low carbon generation technologies (renewable energy, nuclear, and CCS) and 2) district heating systems based on heat networks and distributed heating based on end-use heating technologies. Overall, the proposed modeling demonstrates that the integration of the heat and electricity system (when compared with the decoupled approach) can bring significant benefits by increasing the investment in the heating infrastructure in order to enhance the system flexibility that in turn can deliver larger cost savings in the electricity system, thus meeting the carbon target at a lower whole-system cost.