How can I prevent mould growing in a built-in wardrobe?

I downsized into this house about ten months ago, so I have a lot of stuff to sort through. There are two built-in wardrobes against outside walls which I have filled with bedding, boxes, files etc, and now find that damp has accumulated in the full-up, closed wardrobes, and mould is growing in the damp conditions. I know that I should have insulated the cupboards, and am now about to do it, but have had to stop because I have found the mould. Is it too late? Will it work? Will it simply hide the problem and allow mould to grow between the wall and the insulation?