How much does it cost to run?
In our experience so far, our heat pump has cost us slightly less than heating our home with gas. Though a heat pump is several times more efficient than a gas boiler, electricity usually costs 3-4 times more than gas. So while we use less energy to heat our home, our bills usually work out to about the same over the course of the year.
Of course, energy bills will be much higher in winter. The chart below shows how January can account for nearly 20% of the annual costs of running the heat pump, but July and August were less than 1%. So your bills could be £200 in January, but less than £10 in summer.

What funding is available?
This might take a little bit of digging, to figure out what exactly is available to you. A top line summary (for those in the UK) looks something like this:
England + Wales: £5k grant. Installer applies for the grant and takes it off the install cost.
Scotland. £10k loan, which you apply for before the install. You need to pay the installer the full amount, then after it's installed you get the £10k, and gradually pay back £2.5k.
Read more on EDF's website.
Tips for bringing down energy bills
Heat pumps are most efficient when outputting lower temperatures than gas boilers. This doesn’t mean the house is colder; it just means the radiators are warm all day instead of pumping out high heat for a few hours at a time.
Radiators with bigger surface areas, or even better - underfloor heating - are great if you have a heat pump. The added benefit of this is the house stays warm all day, and the radiators are much safer to touch.

Generating and storing your own electricity is another great way to bring costs and carbon down. Even in February in Scotland, our solar panels are covering more than 20% of our electricity on some days. As we move into spring, this will climb steadily higher.
Combining solar panels with home battery storage will reduce the amount of energy you pull from the grid, and can reduce electricity bills to almost nothing during the summer months. You can also sign up to an electricity tariff with a cheap night rate and charge these batteries when the price is lower.
Doing so also helps the grid by reducing the amount of power used at peak times (usually 4-7pm), when the dirtiest power stations get used to fulfil demand.

Does it work??
'It’s been proven that heat pumps don’t work in the UK'
This is a comment I saw written under an article about heat pumps recently. I can now ‘prove’ this commentator was completely wrong! Unless I’m mistaken, I’m writing this on a stormy February day, in Scotland, in an old house, heated purely by an air source heat pump, and I’m feeling toasty warm and happy our house no longer needs to be run off fossil fuels!