This work considers the potential reduction in the carbon dioxide emissions associated with the operation of Air Source Heat Pump which could be achieved by using demand side management. In order to achieve significant reductions in carbon dioxide emissions, it is widely envisioned that electrification of the heating sector will need to be combined with decarbonisation of the electrical supply. By influencing the times at when electric heat pumps operate such that they coincide more with electricity generation which has a low marginal carbon emissions factor, it has been suggested that these emissions could be reduced further. In order to investigate this possibility, models of the UK electrical grid based on scenarios for 2020 to 2050 have been combined with a dynamic model of an air source heat pump unit and thermal models of a population of dwellings. The performance and carbon dioxide emissions associated with the heat pumps are compared both with and without demand side management interventions intended to give preference to operation when the marginal emissions factor of the electricity being generated is low. It is found that these interventions are unlikely to be effective at achieving further reductions in emissions. A reduction of around 3% was observed in scenarios based around 2035 but in other scenarios the reduction was insignificant. In the scenarios with high wind generation (2050), the DSM scheme considered here tends to improve thermal comfort (with minimal increases in emissions) rather than achieving a decrease in emissions. The reasons for this are discussed and further recommendations are made.