Is the answer just to wash everything in it? It's a built in wardrobe in an old council house.
I've been keeping some of my "for when I lose the weight" clothes in there, I'm going to just get rid of them but I have my DD's dresses and coats hanging up in there and would like to et rid of the smell!
If the wardrobe is built into a wall that is external (on the outside of the house) then the musty smell might be some condensation damp and you could get get black mildew on the clothes if you continue to store them there. In that case it would be best not to use the wardrobe or you might need to keep a door open to create airflow or use dehumidifying crystals.
If the wardrobe is on an internal wall then it might just be stale. I would wash the inside and rails down with a mild disinfectant or bicarbonate of soda solution to remove smells. Let it dry (and perhaps repaint the inside if paper/plaster on the wall bit). Keep the doors open and hang some lavender sachets or use a reed diffuser in it and see how it goes.