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Respectfully disagree. Modern inverter driven HPs are very quiet (I've worked in HP industry for fifteen years). I'm literally putting one in my own apartment at the moment however my outdoor unit will be in the garden as it's a ground floor apartment.
Depending on whether @revenant. can put anything on outside walls the outdoor unit could be wall mounted too... they're basically just an AC unit (of sorts and size)...
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I’m about to embark on a ground-floor extension of a Victorian semi, and want to de-gasify the place.
What kind of costs all-in, including any grants, would I be looking at to install an external AS heat pump system, to heat a ~120m2 house?
Could mount the unit onto our exterior wall in the side passage between the neighbour’s...
Speak to a qualified supplier & installer.
Heat pumps are obviously a no-go if it's a flat, and an internal ASHP would be a terrible idea - they're not quiet and you'd be sacrificing valuable floor space to a noisy metal box...
Electric UFH would be good for heating a bathroom (Schluter do a good ditra-mat combined soultion), and you could also put in an electric-only heated towel rail, but heating a whole flat this way would be inadvisable. You want an electric boiler heating water for wet radiators.