As it's only in heavy rain I'd bet money it's that back edge where the roof slopes towards it. Ours is exactly the same. The flashing just gets overwhelmed due to the sheer volume of water swirling about in that triangle behind it. It's usually only a brick or two high, plus you can't see how far up the slope it goes. Water could be going under the slates, round the lead then wicking back into the chimney.
Go in the loft and look the next time it rains heavily. Or even just looking outside you may see the pool of standing water there.
Our chimney is going this year, have had enough of the stupid thing, we don't want to burn stuff and it also causes a massive draught from the living room.
It might be worth checking if your neighbours actually want it, you never know they may be glad to get rid of it too.
Go in the loft and look the next time it rains heavily. Or even just looking outside you may see the pool of standing water there.
Our chimney is going this year, have had enough of the stupid thing, we don't want to burn stuff and it also causes a massive draught from the living room.
It might be worth checking if your neighbours actually want it, you never know they may be glad to get rid of it too.