How Much Does It Cost To Move A Heat Pump . If the environmental taxes were removed from electricity, your heat pump would cost £100 less to run than a gas boiler. As you may know, heat pumps aren’t cheap. Today’s Heat Pumps Are More Efficient And CostEffective Than Ever Before from www.uniqueheatingandcooling.com If the environmental taxes were removed from electricity, your heat pump would cost £100 less to run than a gas boiler. Let's look more closely at each type of heat pump. Most companies charge a flat rate for specific.