I am responsible for an office ASHP heating system, and this morning when it's 2 degrees C outside, the outdoor unit is continually icing up. For 20 minutes of each hour it produces no internal heat as it it busy defrosting its outdoor coils. Even though the building is well insulated and has been Environmentally Certified as BREEAM Excellent; once the outside temperature drops to low single figures it can only maintain 20 degrees internally with the ASHP running 24/7.
Because ASHP's work like a fridge in reverse, the indoor coils get warm, and the outdoor coils get cold, so even when it's 5 degrees C outside the outdoor coils will still ice up as the coils themselves fall below 0 degrees C, and the damp British air passing over them turns to ice.
When it's 10 degrees or above outside it produces vast amounts of heat and warms the building very quickly, but as the temperature falls into single figures and more heat is required, efficiency drops and it produces much less heat, and then when we get down to 5 degrees the dreaded defrosting starts.
So in summary, at the point when you need more heat, the ASHP heat output drops dramatically.......
Having said that, it's a good few years old now though, so maybe the new technology is a bit better, and GSHP's wouldn't have the same problem, but they aren't viable for most UK homes.
A friend of mine installed an ASHP at home 2 years ago, and whilst he's reasonably happy with it, he said that when connected to radiators the heat pumps only make them warm, not hot like a boiler. So, he had to have some additional radiators installed and some existing ones replaced with new ones that were twice the size. This low temperature is fine for UFH though, so good for new builds, but that won't help most homeowners who would find it a massive undertaking to install the required water pipes, manifolds and insulation. Regarding the running cost, he says whilst it uses less energy to run, because the cost of electricity is higher, the overall running cost is the same as for his old boiler.