the projecting part of the wall looks like it might be a chimneybreast. These are often full of builders rubble, which will draw water up from the base much more than good clean brickwork. It may have no DPC, probably in the belief that an open flue and constant coalfire would keep it warm and dry. I think I can see efflorescence and old frost damage which may be related. Luckily, it can be fairly uncomplicated to open up a bricked-up fireplace and shovel out the rubble (preferably go down below floor level) and add an airbrick to ventilate the chimney and help it stay fairly dry. Drilling into the fireplace and prodding will indicate if there is damp rubble inside. A disused fireplace, opened up and ventilated, can make a useful wine store.
I would be very inclined to take up the paving, reduce the ground level, examine and probably replace the broken drains. That would reduce the excessive water load, and lowering the ground level will expose more bricks so they can lose water by evaporation, instead of soaking it up. Water rises into bricks until loss by evaporation equals water entering from below, though the mortar joints between bricks also inhibits capillarity due to change in pore size. If the drains are leaking and splashing they will add a lot of water to the ground against the wall, which would correspond to the wet area in that corner beside the gully.
if, as I suspect, there is an original slate DPC somewhere in that wall, lowering the ground level below it will make it much harder for the wall to be damp above it. look out for the floor also bridging it, though.