I've had a search and cannot find anything on this...
I've a late cooper with walnut dash. It has a little water damage from when it is on the road last time around. Not bad by any standard, in fact, it's in better condition than many.
I seem to remember reading somewhere that you can deal with this with a warm iron, a wet towel and a lot of care. It sort of makes sense, melt the adhesive reattach and the towel stops you damaging it further.
Has anyone done this successfully? I'm nowhere near brave enough to try it cold!