D
Deleted member 23452
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Can you get one where the roof meets the back wall of the house?
It's a shallow pitch, so the lead should be two bricks above the point the roof meets the wall. If I've got my bearings right then the damp patch on the ceiling is on the opposite side to the back door at the furthest end from the house. If water's getting in at the joint between the house and the extension then that's where it would run to. It looks like the gutter joint just to your side of the soil stack vent is gobbed up with sealant or mastic, if that's leaking or overflowing then it'll put loads of water down at that point when it rains.
Does the soil stack run down through the extension roof? If so, have a look at the collar and joint where it goes into the roof.