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It's better for sure, but we were starting out from a very low base - we had an old immersion heater system, powered by gas, with very inefficient single bar radiators. Too early to be sure about cost savings (especially given that it's recently gotten cold so our energy usage profile has changed correspondingly) but we've gone from using 80% gas and 20% electricity to the opposite; and we're having to set the thermostat much lower to get to a comfortable temperature.
One thing to bear in mind - you'll have probably a few days during install where you don't have any heating or hot wat. That sucked in October but suspect it'll be worse in December. They'll bring mini heaters which help but try to be out of the house as much as you can during the middle part of the install if you've got the option.
We just had a heat pump installed last week, using Octopus and the £7500 bus grant. They upgraded all our radiators at the same time, I think in total it cost us around £2300. Some snagging issues which I'm hoping they'll work out.
If anyone's considering buying one and is interested in the process or my experience please shout, happy to share.