Back to practicalities. For an air pump to be sufficient, yuo need a well-insulated house. I was brought up in a rather nice, 3-bed new build council semi with a big garden at the back and a smaller patch at the front. Lovely, but chilly with it's livingroom coal fire, nothing in the dining room and a coke boiler in the kitchen which heated the water in the winter. My bedroom was unheated. We used a very unsafe parafin heater in the bathroom. Chilblains at night, frost patterns on the inside of the living room windows in the morning. Poor insulation. Those houses still in Social use have been having insulating cladding added externally, installed by the Housing Association. They will have had their attics insulated as well. But the windows are 25 years old. Not the best, although still better than the single glazing and draughty wooden surrounds they were built with. Plenty of room for an air pump, probably room for larger radiators and tanks. But I read a few days ago that many houses around the country with the cladding installed about 3 years ago are now smothered in mold internally and the cladding must be redone. Any small gap lets water in and traps it.
My 1970s Wimpey's no-fines "solid" wall property has an extra radiator in the livingroom, insulation in the attic, top quality double glazing and leak free external doors (paid for by me, after I bought it). The walls should have been 12" thick to insulate them, but Council budgets meant that they were built only 8" thick. My research indicates that there is NO WAY the insulation of the walls can be safely improved. There were a lot of these houses built. My elder daughter and SIL own a 3 bed version and have problems keeping it warm even with a new boiler and plenty of money to pay the bills. Their garden situation is even worse than mine. They have the "Patio door" version at the back and an even smaller, North facing garden. These houses, both the no-fines terraces and the older, breeze block semis are everywhere in the country, in their hundreds of thousands, perhaps millions.
I can afford my current bills. OAP and widow's work pension. I heat the livingroom. The rest gets no heat except the bathroom for a bath when I need one and in the very coldest weather the bedroom for a while before bed. I have hot water 2 days a week and a gas cooker. I pay £70-£80p.m. at present, dual fuel. A heat pump is designed to run continuously day and night, summer and winter, with electric "panels" kicking in if the 35C flow temp can't be reached otherwise. Heat in winter, AC in Summer. How the hell would I pay for that?