Fuel poverty is most prevalent in North East England with 14.4% of fuel poor households in Newcastle upon Tyne. The aim of this paper was to identify a grid connected renewable energy system coupled with natural gas reciprocating combined heat and power unit, that is cost-effective and technically feasible with a potential to generate a profit from selling energy excess to the grid to help alleviate fuel poverty. The system was also aimed at low carbon emissions. Fourteen models were designed and optimized with the aid of the HOMER Pro software. Models were compared with respect to their economic, technical, and environmental performance. A solution was proposed where restrictions were placed on the size of renewable energy components. This configuration consists of 150 kW CHP, 300 kW PV cells, and 30 kW wind turbines. The renewable fraction is 5.10% and the system yields a carbon saving of 7.9% in comparison with conventional systems. The initial capital investment is $1.24 million which enables the system to have grid sales of 582689 kWh/a. A conservative calculation determined that 40% of the sales can be used to reduce the energy cost of fuel poor households by $706 per annum. This solution has the potential to eliminate fuel poverty at the site analyzed.