There may be another reason why your lounge is colder, the rad is under the window, I am aware this is common practice however when it is hot it has no thermal mass above it to hold the heat (no brickwork just a window), all the other rads will warm up the wall above the rad acting similar to a storage heater.
I would just like to simplify this thread for some reading, because due to more government rules it may sound like rocket science to some.
The temperature you are trying to achieve is around 20 degrees, a gas boiler would run at around 65 degrees, taking into account some system heat loss your rads would be around 55 degrees.
If you change to a heat pump they run at lower temperatures, so to maintain the 20 degrees you require you need to have reasonable insulation, the less heat you let out the less you have to put in, also to warm the rooms from cold you would need a larger surface area of rad to heat the same room space because they would be running slightly cooler, still a long way from the 20 degrees you are trying to achieve though.
I have seen several different heat pump systems here in the UK, and most are working very well, some had initial problems but this was due to install plus fine tuning as they are quite complex, sadly the worst one is a local authority house, installed by people that do not understand how they operate so the plumbing/wiring was all quite shocking really.
As to the running costs, I can give a direct comparison here, two friends of mine have similar houses, one is slightly older and uses oil to rads, heating costs £2500 per year, and it is not too warm in there.
The other house is new, well insulated, underfloor heating and a ground source heat pump fitted, heating cost £900 per year, and it is very warm in there. The system was not without its problems in the first 6 months though but well worth the hassle.
The advantage of an ASHP is that it stands outside and if you choose the right make they are very quiet, but for a GSHP you have the added cost of installing your ground collector, whether drilling or laying a grid, plus the inconvenience and mess, you will also need a plant room to put the heatpump and associated hardware.
So normally, not always but normally, ASHP is best for retrofit, but GSHP is best new build.
One other thing that I would recommend, is to have your property surveyed with a thermal imaging camera, but by someone that knows what they are doing, it is a fantastic way to find out where the heat is escaping from your property and some of the remedies may not be too expensive.
I hope this helps.