Heat pumps in UK are mostly air to water and integrate into your central heating They do not offer cooling, so no need in ducting to every room.
UK problems are around retrofitting housing stock never designed with an idea of a unit outside. For example the logical place for me to place a heatpump is roughly more than 8m away from where the water tank would be. So you would have to run ducting outside of the house.
And thats after i took out a door and walled that in (with eventual upgrade to heatpump) to leave the space specifically for the heatpump.
So alot of the extra cost would be working around ducting it to the place where it integrates into existing heating system.
We tend not to have air-conditioning either, housing stock can suffer from condensation and mould easily here. As its old and never designed for modern standards. Mine is about 130 years old or so.
So all in all, its a right pain to do.