Re: Change that to "Fossil Fuel Giants and anyone who buys their products"
The big factor is how efficient your gas plant is. The UK averages around 49% thermal efficiency for its gas power plants (through heat recovery) which is rather good, compared to straight gas turbine generation (around 30%):
https://www.gov.uk/government/statistics/electricity-chapter-5-digest-of-united-kingdom-energy-statistics-dukes (DUKES5.10)
A report from around 2014 mentions that national transmission losses are 8%
https://publications.parliament.uk/pa/cm201415/cmselect/cmenergy/386/38607.html
Therefore, the heat pump needs to hit a CoP of 2.2 to break even with a gas boiler. This is quite achievable but does fall when the temperature drops (for air source, ground source does much better and is less subject to atmospheric temperatures).
The other factor for the end user is the cost of electricity vs gas. If you're on mains gas, you're looking at around 3.5-4.5x more for a kWh of electricity than a kWh of gas but those off the gas network suffer from a much smaller difference. Basically, at the moment, if you're have mains gas, you either don't care about paying more (before even considering the cost of installation), you are very wealthy and can afford a ground source heat pump or you're banking on that window closing over the lifespan of the heat pump.
Personally, I believe the government shouldn't have limited heat pump subsidies to heating-only systems based on water radiators. If people could get air conditioning into the deal, they'd probably have been more enticed.