Advice on caravan curtains wanted please

We have found a line of black mould/mildew on the lining of our front caravan curtains (the curtains that have the plastic hems with poppers top and bottom that fit into the tracks), has anyone got any advice on how to clean the mould/mildew off?  In the caravan manual it states that the curtains should be dry cleaned only so I am reluctant to wash them in case they shrink, it is only the lining that is marked not the curtain itself.

I would appreciate any help and advice that you can give.