Cut out all the sections of  the blackberry plant that is showing the fungus. Wet, warm weather causes the spread of the fungi so once the summer weather arrives you will see less problems. A fresh mulch on top of the soil will help to seal in the fungal spores that may have fallen to the ground. Good air circulation helps to keep the plants healthy so thin out the plants if you have allowed them to grow into a thicket. Try to keep the foliage dry by avoiding overhead sprinkling. Do not let the plants dry out as stressed plants are more susceptible to fungal infections. Blackberries can handle a heavy pruning so I predict you will still enjoy blackberry pie just later in the season. Keep growing, Marianne Binetti