Could be;
poor flashing where roof meets chimney
roof at chimney junction may have collapsed slightly with persistent
damp - channeling storm water which can blow through tile gaps
open chimney gets wet inside and out and becomes soaking wet
permanently, especially if it isn't used or only used for gas
appliances.
If not used it wants capping with ventilating clay mushroom pot - not
enough to just put a slate on top with a few holes, AND also
essential is a good vent from the outside as low down as you can get
- to generate a good flow through of air. Perhaps removeable so that
you can remove debris and old soot.
Or if not used could be removed entirely and roof covering continued
over
If used then cap with good chimney pot and repoint, reflash with
proper traditional stepped lead flashing and soakers.
If you can get up there inside the roof with a torch during a heavy
downpour such as we have been having lately you might see the source
of damp unless its just soaking in through the masonry.
Whatever the cause the moisture comes from the outside, there is
nothing very effective you can do from the inside to stop it except
perhaps good pointing to the chimney breast up to the roof.

cheers

Jacob