The rollout of smart meters raises the prospect that domestic customer electrical demand can be responsive to changes in supply capacity. Such responsive demand will become increasingly relevant in electrical power systems, as the proportion of weather-dependent renewable generation increases, due to the difficulty and expense of storing electrical energy. One method of providing response is to allow direct control of customer devices by network operators, as in the UK `Economy 7` and `White Meter` schemes used to control domestic electrical heating. However, such direct control is much less acceptable for loads such as washing machines, lighting and televisions. This study instead examines the use of real-time pricing of electricity in the domestic sector. This allows customers to be flexible but, importantly, to retain overall control. A simulation methodology for highlighting the potential effects of, and possible problems with, a national implementation of real-time pricing in the UK domestic electricity market is presented. This is done by disaggregating domestic load profiles and then simulating price-based elastic and load-shifting responses. Analysis of a future UK scenario with 15 GW wind penetration shows that during low-wind events, UK peak demand could be reduced by 8-11 GW. This could remove the requirement for 8-11 GW of standby generation with a capital cost of £2.6 to £3.6 billion. Recommended further work is the investigation of improved demand-forecasting and the price-setting strategies. This is a fine balance between giving customers access to plentiful, cheap energy when it is available, but increasing prices just enough to reduce demand to meet the supply capacity when this capacity is limited.