I suppose it depends upon what the loft insulation is made of. I can imagine that it is highly absorbent so may pass even more water into pots such as terracotta? The other consideration is if it has glass fibre in it. I wouldn't use it if it has. Someone else might be able to help further.

We have the foil covered stuff in our loft. I suppose it would be a good idea, as long as it is sealed up at the ends. I used foam pipe insulation on a standard fuscia stem, as I have no greenhouse. It well worth experimenting with various methods to preserve tender plants you want to keep. Lots of layers of bubble wrap is another ploy perhaps?

Yes Dorjac the type I have is the same, The fibres are sealed within plastic with foil on one side the same as what is in your loft, So I could use it I imagine to wrap the pots in to prevent the roots from frost, and protect the rest of the palms with bubble wrap, Is there any advise anyone can give on how to better protect the leafy parts as they are quite big and too expensive to lose.
I also have a Banana Tree to consider, Maybe straw?

I agree with Fractal about it's absorbency, this could freeze doing even more damage to your palms!