Abstract Increasing demand-side flexibility is important for decarbonising electricity systems with increasing intermittent and variable renewable energy. Although previous research has identified reduction of carbon emissions from electricity consumption as a driver for households to provide demand-side flexibility, it is not clear yet whether they are willing to provide additional flexibility if the emission reduction takes place locally. This study conducted an online factorial survey across the UK to investigate the determinants of domestic consumers' willingness to participate in time-of-use and direct load control of electric vehicle charging and heat pump heating programs. The results show that consumers generally prefer the static time-of-use tariffs (programs) to more flexible, controlled charging/heating programs (e.g. vehicle-to-grid charging), but savings on electricity bills, the percentage of reduced carbon emissions, and localisation of emission reduction (i.e. contributing to local emission targets) can significantly motivate participation in demand-side flexibility programs. Keeping other variables constant, localisation of emission reduction can increase the likelihood of program acceptance by over 11\%. Socio-demographic variables (e.g age), energy-related behaviours (e.g. intention to buy an electric vehicle or a heat pump, the current expenditure in electricity), consumers' trust in electricity service suppliers, their concerns over data privacy, and attitudes towards climate change and local carbon targets also influence household willingness to provide demand-side flexibility.