Air Source Heat Pump limit of Coefficient Of Performance being less than one?

The coefficient of performance can certainly be less than 1, as you will see from any thermodynamics text book. The COP is directly related to the ratio of input and output temperatures, as this becomes bigger the COP falls dramatically. The whole heat pump thing is driven by misconceptions and assumptions, because mechanical and heat losses in the compressor are rarely taken into account and as the COP becomes smaller  become very important. The easiest way to understand this is to examine any engine that depends on combustion, how efficient is your car engine, or a jet engine or anything similar. All of these use exactly the same thermodynamics, and you will find that the efficiency of an engine rises as the temperature differential across it gets larger. This is why power stations use super-heated steam at a very high temperature and operate into cooling towers to make the exhaust temperature as low as possible, the same for gas turbines, the fuel is burnt at as high a temperature as possible (given practical materials for combustion chambers and turbine blades) and operate into as much of a heat sink as possible, typically a low temperature combined cycle boiler.

For heat pumps the input and output temperatures are critical to the COP, given underfloor heating as the output and a warm day as input the COP can be very high, 10 or maybe more. BUT if the cold end temperature is -10C and the output to radiators at 60-70C (less than normal CH BTW), the COP will be less than 2 with practical working fluids. This is another point, the best fluids tend to be ammonia (very explosive) or flourinated hydrocarbons (banned as being greenhouse gases!). This also reduces the temperature range available and the COP.

The coefficient of performance can certainly be less than 1, as you will see from any thermodynamics text book. The COP is directly related to the ratio of input and output temperatures, as this becomes bigger the COP falls dramatically. The whole heat pump thing is driven by misconceptions and assumptions, because mechanical and heat losses in the compressor are rarely taken into account and as the COP becomes smaller  become very important. The easiest way to understand this is to examine any engine that depends on combustion, how efficient is your car engine, or a jet engine or anything similar. All of these use exactly the same thermodynamics, and you will find that the efficiency of an engine rises as the temperature differential across it gets larger. This is why power stations use super-heated steam at a very high temperature and operate into cooling towers to make the exhaust temperature as low as possible, the same for gas turbines, the fuel is burnt at as high a temperature as possible (given practical materials for combustion chambers and turbine blades) and operate into as much of a heat sink as possible, typically a low temperature combined cycle boiler.

For heat pumps the input and output temperatures are critical to the COP, given underfloor heating as the output and a warm day as input the COP can be very high, 10 or maybe more. BUT if the cold end temperature is -10C and the output to radiators at 60-70C (less than normal CH BTW), the COP will be less than 2 with practical working fluids. This is another point, the best fluids tend to be ammonia (very explosive) or flourinated hydrocarbons (banned as being greenhouse gases!). This also reduces the temperature range available and the COP.