This is a really common problem because so many people live in small gardens with high-sided enclosures.
Older walls are more porous and act like wicks, drawing the moisture up which then evaporates off.
Consider painting the wall or fence, but choose the colour carefully, because if you paint it blue, it will completely influence what colour plants you choose. There are things like winter jasmine, all the ivies, some of the climbing hydrangea - or the Euonymus fortunei radicans is another one that will tolerate quite a lot of shade and will stay green and at least look all right. It looked wonderful. Pippa Greenwood One plant which I think always does very well on a north-facing wall is the hardiest of the azaras, Azara microphylla . It's got lovely little vanilla perfumed flowers which are a lemony yellow colour in early spring.