Condensation in converted cellar.

[MacLaverty]

We moved into a 120yr old property 15 months ago which has a converted cellar. Unfortunately the cellar has not been done properly as has no waterproof membrane on the walls, no sump pump etc and is simply tanked with a timber frame, plasterboard and wall insulation off the old external walls. We do not have the money to have it all ripped out and done properly unfortunately but it was done 4/5 years ago and the main room is still dry so something must be working. However, I have discovered that a part of one external wall near to the floor behind the plasterboard is wet to the touch where the insulation does not touch the external wall, picture below. It is not dripping or causing issues as far as I can tell but would adding insulation to fill the void completely stop the condensation forming or would it simply give a route for the condensation to soak into the insulation and eventually the plasterboard and I am best keeping the air gap as currently is?

Also, we have a cupboard down there and in warmer months after it has been raining one corner gets very wet due to the humid air coming in from the vents. Would drilling holes in the cupboard provide adequate ventilation or would this have neglegible effect?