If you switch out the gas boiler for a heat pump, it can still heat the hot water and heat the central heating loop. But it can't provide cooling that way. There is no infrastructure in most houses to run AC ducting or refrigerant pipes.
You might think that you could simply cool the water in the central heating loop, and therefore make all of the radiators very cold, and use that to move heat out of rooms. In theory that might work, but in most houses these central heating pipes are not insulated and run under floorboards. If you make them cold then they'll cause condensation, leading to water in all kinds of small spaces, and likely leading to warping, damage, or mould.
In the UK, retrofitting AC into an existing house is a huge undertaking in most cases.
The average US household uses 10,000 kWh annually ~833 kWh per month. So I'm guessing most Americans reading the article and looking at the interactive graph are thinking either: this is very cheap or very expensive, depending on whether they are assuming it's monthly or annual.
In the US the average price for 3100 kWh in California would be $1062 which is among the highest in the continental US. So right in line with GB.
In New York it would be $710. Florida it would be $454.
So it's high, but not as eye-watering as it seemed to me initially.