I went through a lot of thinking and investigating before replacing our 35 year old oil boiler last year. No gas in this village. I ended up with a new much more efficient oil boiler and much better controls, got the best 'blueflame' technology available at the time. I reckon last winter we used much less oil - you never can tell because winters vary - but maybe 25% saving, a bit via boiler efficiency and a lot via better controls.
So why not ASHP? The reasons others have alluded to: the temperature differential (radiator to air) is much less so you need to have bigger radiators - disruption in every room inclusing major layout changes - and/or an always on system> The house isn't terrible but to make it work I would have needed much better windows and insulation so the total cost would have been 2 or 3 x the ASHP cost, and a general worry about being wholly dependent on electricity for heating - with oil I do have some choice about when and where I buy it. There is also the curiousity that ASHP is less efficient (input vs output) in the coldest weather. So on balance, and with some guilt, I didn't do it.
A smaller house, new build and/or higher insulation standards and certainly if designed in and installed from day 1 it should be a clear ASHP (or ideally GSHP) choice, but for most of us we have to balance environmental responsibility with financial reality. I couldn't afford to do the job properly.
I have seen some hybrid systems, essentially ASHP for most of it and an in series oil or gas boiler and a brain which tells the system which to use. That might help in older properties, but the very good engineer who came to quote and do the job (known him years, not an "energy consultant") shook his head and said that I would be paying lots for ASHP but the boiler would still run a lot of the time.
A few ski resorts built in the 1960's, like Flaine in France, and most urban housing in former eastern bloc countries, have a centrat boiler house or two. You don't buy gas or electricity, you buy heat. That strikes me as a way to go for dense housing - the operator can use the most efficient technology and update it as required, even having multiple technologies and using the one that makes most sense 'on the day'. Power and fuel distribution gets a lot easier too.
Truth is, the people that live in the least efficient draughty damp houses where ASHP woudl make a real difference can't afford to do anything about it. Some can't even afford LED lightbulbs even though they repay themselves in just a few winter months.
(Listening to Johnson though gives me an idea. Maybe I should go that route - I will give Lord Brownlow a call and see if he will stump up a few £££ to install and a few ££££ for new wallpaper afterwards.)