The RNLI, Mountain Rescue and other groups working alongside certainly aren't being paid overtime. Or any salary at all, come to that.
The RNLI and MR etc are not obliged to turn out - they are volunteers (albeit very worthy volunteers). I myself am a volunteer in my local civil defence cadre here in France and turn out for them whenever I can.
It is a different sort of sacrifice to military who, when on rare occasions are ordered to turn out to supplement the civil defence forces, have no choice in the matter (even though they are usually very keen to help anyway). It is quite right that they should be compensated for their lost leave.
European countries are, for the most part, well managed and have a good balance between volunteer community spirit and state resources. If we regress to a system where there are no volunteers and no community spirit, we will be going backwards to the dismal levels of other parts of the world.