If it’s on loft legs, it will be 250mm or more so you are good there.
Air to air heat pumps are what you’d typically describe as ‘air conditioning’, modern ones can heat at very high efficiencies.
You have an outdoor unit which can run multiple indoor units which are usually wall mounted cassettes.
What most people don’t realise is that you can get ‘indoor’ units which you can mount in your loft and then run to multiple rooms via ducts so you can heat the entire top floor with no visible infrastructure other than a small vent in the ceiling. If retrofitting downstairs you’ll have normal wall cassettes, manufacturers are making more of an effort these days to make them look vaguely stylish.
Air to air heat pumps can now also heat hot water cylinders although you can continue to do that via an immersion.
When heating air, they can typically reach a seasonal coefficient of performance of 400% (seasonal meaning a year round average). That means for every 1 kWh of electricity you put in, you get 4 kWh of heat. Storage heaters are 100% in that for 1 kWh of electric you get 1 kWh of heat.
As Simon said, the payback period will be measured in years but there will be one. Decent storage heaters are not exactly cheap to replace either.
You also then have air conditioning for the summer and you don’t need to do every room, just the ones where it makes the most sense.