cold damp corner with a dry sump
To make long story short from what I see my best guess is that you have condensation issue. Most likely since your pump is in the corner there is somewhere thermal insulation missing and since you said that there is draft that means cold air is coming inside. Where from?.... I cannot be 100% sure. My money would be on the wall because most likely places where pipes are going through the wall aren’t insulated, but since you said that you are feeling draft is coming from the floor maybe something is happening over there. Anyway placing thermal insulation under the pump (best if possible) and on the places where there are pipes should fix your problem.