Would a heat pump cost less to run?
An air-source heat pump turns one unit of electricity into roughly three of heat. Whether that beats your boiler comes down to your heat demand, the unit's efficiency and your tariff. Here is the comparison, with the £7,500 grant included.
Gas factor 0.183, electricity 0.207 kgCO₂e/kWh (DESNZ 2024). Install ~£11,500 before grant.
The comparison, step by step
Your home's heat demand is the heat delivered into the rooms each year. Your boiler burns more fuel than that, because it is not 100% efficient, so your current cost is heat demand divided by boiler efficiency, times your fuel rate.
The heat pump delivers the same heat using electricity equal to heat demand divided by its SCOP. At a SCOP of 3.4, 12,000 kWh of heat needs about 3,530 kWh of electricity. Multiply by your electricity rate for the running cost.
The result is the difference. Against mains gas on a standard tariff, a heat pump often lands close to level; a heat-pump tariff usually tips it cheaper. Against oil, LPG or electric heating it is normally cheaper to run. We take the £7,500 grant off the typical £11,500 install.