As above, merino wool garments are worth looking at and if 100% wool will irritate you, you can get a blended garment.
Kitting out the entire family in pure merino base layers will certainly help keep you warm, but will cost you a bob or two (£100 - £200). If cost is an issue, you may want to have a look at cheaper blended clothing.
As a renowned cheapskate and bargain hunter, it will not be much of a surprise that the recommendation I am going to give you is a low cost option, but you (and other reading this) might appreciate it.
Mountain Warehouse do very reasonably priced 80/20% Merino / Polyester base layers, which have helped keep me warm in -0 temps. And being Mountain Warehouse there is usually some deal or other, BOGOF, BOGOHP etc that often let you get a blended top and bottom for the same price as just either a 100% top or bottom.
Now obviously the far south west of Cornwall is not likely to experience the same low temps as northern Scandinavian, so if a native or frequent visitor says shut up you numpty, cheap is not an option, I will happily defer to them. But if you are sensibly applying the layer principal (ideal with existing clothing so no extra last minute expense) then an option worth investigating?
Regardless, happy shopping and enjoy your trip