Efficiency can be improved by using heat pumps, or limiting when the rooms are heated, there is a trade off with the low cost of off peak to low energy use with as required. There are hot water heat stores which lose less when heat not required but they take up room.
The efficiency of an electric heater is how much is lost when the room is unused. So a room used for one hour and a heater which needs to be on for 7 hours is 1/7 = 14% efficient, likely it does not need a full 7 hours to reheat, so better than 14%, so a fan heater which needs to switch on 10 minutes before room is up to temperature, is 86% efficiency if room used for an hour, room used for 3 hours and 95% efficiency using same fan heater. This assumes you need full output all of the time which is clearly not correct, but this is just to show where the efficiency figures come from. As already stated what goes in must come out with electric nothing goes up the flue.
So much is down to building insulation and life style. This house turn off heating at 10 pm and house only drops 3 degrees by time it switches on again in morning, in the caravan 1/2 hour and it's cold, so timed heating in caravan really saves money, in the house leaving on 24/7 would not affect the bill that much.
The big problem with storage heaters or under floor heating is to work out what the next day or even next 12 hours weather will be like, unless using a well insulated heat store like the water ones, heat is being delivered into the home even when not required.
So cure is experiment, as you can't really work it out, so an energy meter and fan heater and only heat rooms as and when required and then work out how much it uses, then you can do calculations allowing for cheaper day rate using fan heater and cheaper night rate using storage heater. Retired as I am so in the house all day storage heaters would likely be best for me, but if at work during the day likely a more instant type.
In some flats gas is banned, after Ronan Point, but while house hunting found a lot using bottled gas and standard central heating boiler, also of course oil and massive LPG tanks. Then you have to consider if you have the room for a boiler and storage for fuel.