(Note I over-stated the prices by a factor of TEN (ouch!)in the orginal post, due to, er, human error on my part.  The correct figures (I added them in an addendum post) are:

Electric underfloor heating mat = approx. £1,400, or approx 2000 euros.

(I quickly check the zeros...yes, they are correct.)

The flat (not mine, one I saw) is between, say 60 - 90 square metres (lots of rooms in funny places, and I'm no good at guessing room sizes), and had no heating system installed (apart from two hundred year old fire places.)

Don't fight forces, use them R. Buckminster Fuller.

Actually, you have the problem of COP<1 only with the "cheap" (that is 5000 €) heat pumps fitted on the balcony, and which try to exchange heat with the atmosphere like an air conditionner. They practically stop working at 0°C because of frost on the exchangers.
"Real" heat pumps take the heat from 1.5 m underground, where it's 10°C almost all year long, with burried pipes (that's where you need a lawn and big work $$$). You may need additional fuel heating a few days/weeks per winter if you are in a really cold area where the ground freezes in the winter (like: there is 20" of snow on you lawn for 2 months every winter...)
There is still a variant to fix this problem: the heat well heat pump, with a few 50-100m wells which get the heat from the waterbed, which never freezes in any  place that actually has grid power (Siberia is a special case...). And you actually need less lawn area to conceal those wells, but they're even more expensive to drill (expect 20-30k€ for a mid sized house - you may have a tax rebate on this in some countries).

Pierre