It could be one of many things i.e. the lead flasing behind the chimney breast (back gutter), soakers underneath the lead flashing, the lead flashing itself or it could even be that the chimney needs repointing.Hi
it will be your flashings - mostly wind driven and the water drives behind the lead skirt around the chimney 99 % of leaks around the chimney area show below in the nearest room below
To fix you will need new flashings or re sealed with lead seal
GarethThis could be a number of things getting up there and having a look in the loft if possible and up on the roof is the only way to diagnose this leak it could be the flashings themselves or could be missing cement pointing from the chase allowing water to run down the chimney and running into and behind flashings or if its roughcasted it could be cracked allowing water in behind the roughcasting or it could be the valleys on each side of the chimney depending in how its constructed and positioned on the roof best bet is to contact a company that provides free quotes and get up there and have a look also in loft iam sure it will be pretty obvious to an experienced roofer once up there@Georgia
water ingress from a chimney could be a number of things.
1. No Cowling to Chimney pot
2. Lead flashing failing
my recommendation would be get builder to inspect
possibly with the use of a “Drone”
also a Chimney sweep may offer additional service & advice so work calling them.