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Is this an apartment or house and how are you fixed for outdoor space? I wouldn't put in electric heating of any sort under any circumstances as it will break you to run it... dig deep and get a heatpump and underfloor heating or wet radiators at least. It'll be more expensive than new electric heating but it will add to the value of the property and be waaay cheaper to run going forward...
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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.
Can anyone advise on boiler and heating systems?
Place we are buying is electricity only (no gas). It currently has wall mounted electric convection heaters, which are terrible, and a heatrae Sadia megaflo boiler that is over 20 years old.
What are the best options for a new electric boiler and heating system? Is electric underfloor viable throughout?