As it happens, things aren't quite as bad as we feared. While there is lots of water on the ground floor, the damage on the upper floor and attic (it's a full-height attic; basically a third floor of the building) is less than expected. However, standing in the attic, you can see daylight through holes in the roof. Lisa sprayed lots of expanding foam into the holes in the hope that it will fill them up and sort of discourage the wet from getting in. (Stopping it entirely is too much to hope for.)
The foam merrily filled up cracks and went out onto the roof. The results from the outside are somewhat amusing-looking.
The two blotches below the plastic-wrapped chimney are where the foam expanded out the holes. You can see where most of the plastic sheeting has torn away.
With a telephoto lens, Lisa got this close-up of the clumps of spray-foam and their external appearance on the roof.
It's a pity that there isn't a hatch from the attic to the roof; if there was, it might well be easier to get at the roof and do the repairs than by the pair of ladders we've been using.