Due to the unique (and in this case shit) construction of my house I’ve got mould spots forming on the back of a roman blind where it has rested against a very cold lintel. I can’t bleach it and I can’t wash it.

Is there anyway of getting the mould off other than drying and brushing it?

It has probably been stained permanently, unfortunately. You could try brushing vigorously with a nail brush while vacuuming with a crevice tool. Don’t inhale the dust.