The electrification of heating and electric vehicles, under present fixed electricity tariffs, is expected to increase the total and peak demand of electricity. One way to provide for these peaks will be for the power plants to be run part loaded during off- peak times, less efficiently, to increase their power production during peaks. Power network reinforcement and new generation capacity will also likely be required to support the additional electricity demand. Demand Side Response, utilising real-time pricing (RTP), is one possible alternative solution. Monetary incentives can encourage users to re-time their power consumption to off-peak periods allowing utilisation of more efficient power plants. In our proposed system, electric heaters in domestic houses autonomously respond to day-ahead RTP (DA-RTP) electricity prices and weather forecasts, thus reducing electricity demand during peaks and user costs while maintaining comfort. We evaluate the benefits of such a system by simulating an electricity market using Agent-Based Modelling. Agents (houses, power plants, energy storage facilities) are all individually optimised using dynamic optimisation. Power plants and energy storage facilities maximise their profits given forward wholesale electricity prices, subject to operational constraints. We use balancing mechanism (BM) dynamic data and part-load efficiency curves to model the power plants' operating characteristics. The building heating controller minimises users' costs subject to DA-RTP electricity prices and flexibility in the users' indoor temperature. We use internal and external temperatures from 823 houses in England to estimate representative thermal building models and heating patterns. Our results show that a DA-RTP pricing structure of domestic electricity could drive up to 24% savings in HP user energy costs, up to 6.7% reduction in average peak electricity demands, better utilisation of more efficient power plants, and lower grid carbon emissions when compared to a fixed pricing structure. All the above grid benefits are achieved while preserving our defined user comfort and, in some cases, improving it.