Calculation is based on:
Heathrow to Madrid, Spain is 1243 km one way.
BEIS - UK Government GHG Conversion Factors for Company Reporting 2020 - Air Travel with RF factor included states 0.378394 tonnes of CO2 per economy passenger for a return flight.
The carbon difference between a heat pump and boiler is calculated as:
A - 13,903 kWh of energy demand for heating and hot water
B - 3.48 heat pump designed efficiency
C - new boiler efficiency of 93%
D - Gas fuel emissions of 208 gCO2/kWh
E - Electricity fuel emissions of 277 gCO2/kWh
Gas CO2 = (A/C*D) = 3.11 tonnes
Electricity CO2 = (A/B*E) = 1.11 tonnes
1-(1.11)/(3.11) = 64%