Chimney roof leak

Sounds like there is a problem with the lead soakers or in some cases tin soakers which are situated underneath the tiles/slate may have been installed incorrectly or corrosion

Could be water penetration through the pointing or the brick or stone work all depends on the brick stone work weather damage and how porous they are if it's render then the same things apply a good water sealer may help hope its helps

Pourous brickwork/render is my thoughts without seeing......

This sounds like porous brick work/pointing/ render. At least 3 options. 2 not guaranteed. 3 remove chimney so no more problems. Hope this helps. Regards Duncan

This could be (as mentioned above) pourus bricks or damaged render/flaunching but if , when the chimney was built, a lead tray was put in on the correct brick course (where the roof meets chimney at the rear of chimney) AND it was dressed correctly, then pourus bricks/damaged render won't make a difference. This basically means that your chimneys lead tray is either damaged or installed incorrectly. A temporary solution would be to treat with a decent weather proofing. For a guaranteed solution , the chimney needs taking down to roof level and either renewing the lead tray and re-building it OR (if the chimney is no longer in use) demolishing beneath roof level and felt, batten and tile/slate over the hole. Hope this helps