I think I would look at your ventilation. Gable end walls are notorious for being cold especially if it faces into the prevailing weather direction. Since your kitchen is against this wall and is a major source of moisture as a result of cooking the likelihood your damp/black mould is a result of condensation. The cure is keep the room warmer and ventilate when cooking, if you do not have a ventilator than open a window. To remove existing black mould bleach does quite a good job.

Richard