Inside, the roof timbers are starting to exhibit traces of something
unpleasant; there are "tide marks", and inside these are scattered blobs
of a white fluff, like a scattering of icing sugar, and very similar to
some mildewy-like stuff I once had on some old leather.

That sounds very like rising damp. Salts are drawn up by capillary action
and when the water evaporates crystals form. It was in my childhood home.
If that is in your roofspace it is hardly being drawn from the ground, so is
there anywhere moisture could be getting in? Could fascia or soffits be
damaged, or even a blocked guttering?