How to get mildew smell out of a coat that can only be washed on cold and not tumble dried?

So I have bomber style jacket which is fine but the stitched on material badge got wet and now stinks of mildew.

If I wash on cold I assume the mildew will not die but also will wear the jacket out a bit. I tried Frebreze which only masked the smell for half a day.

Is there a product I can get in the UK that will kill off the mildew without spoiling the jacket?