Residential variable energy price schemes can be made more effective with the use of a demand response (DR) strategy along with smart appliances. Using DR, the electricity bill of participating customers/households can be minimised, while pursuing other aims such as demand-shifting and maximising consumption of locally generated renewable-electricity. In this article, a two-stage optimization method is used to implement a price-based implicit DR scheme. The model considers a range of novel smart devices/technologies/schemes, connected to smart-meters and a local DR-Controller. A case study with various decarbonisation scenarios is used to analyse the effects of deploying the proposed DR-scheme in households located in the west area of the Isle of Wight (Southern United Kingdom). There are approximately 15,000 households, of which 3000 are not connected to the gas-network. Using a distribution network model along with a load flow software-tool, the secondary voltages and apparent-power through transformers at the relevant substations are computed. The results show that in summer, participating households could export up to 6.4 MW of power, which is 10% of installed large-scale photovoltaics (PV) capacity on the island. Average carbon dioxide equivalent (CO2e) reductions of 7.1 ktons/annum and a reduction in combined energy/transport fuel-bills of 60%/annum could be achieved by participating households.