Lost count of how many times I have seen this! Always a mistake to incorporate an old chimney into a loft conversion.
Ideally, you need to dry-line that area, so those minor dribbles don't interfere with your internal decor.
Some roaring fires will also keep the damp at bay!
I used Halfords a couple of years ago, bought the oil, used it no problem, went again a month ago, used their in-store computer, got home to find it's different from last time!