They work fine on cold weather, Sweden uses a huge number of heat pumps. Less efficient, yes but still very efficient. The main issue is U.K. housing stock is rubbish and poorly insulated.
In terms of insulation, you should be looking to do everything you reasonably can to insulate regardless of getting a heat pump or not. Heat loss is the same regardless of heat pump or boiler and the heat loss will cost you a fortune either way.
You do need an immersion but you only need to boost the hot water tank every now and then for legionella, otherwise, 50c hot water is more than fine for daily use. In terms of rads, normal boiler flow temps are 60-65c and returns below, heat pumps are lower but the temp can be designed into the system. If you have underfloor heating you might want that to be as low as 30c. For rads you want it to be more, perhaps 40-45c and this you need 50% bigger rads but that’s assuming they are the minimum size for the 65c flow temps. It can be as high as 50c but the high the temp the less efficient it is.
Ground source is far better than air but even more expensive. Both are more expensive than gas and you also have to consider what happens when the heat pump brakes or expires outside of warranty and needs to be replaced. They’ll be no grant for that.
