Maybe they're Raspberries ;-)

Are they getting plenty of sun? All cane fruits need a lot of sun to ripen properly.

Are you sure they are blackberries? Loganberries and tayberries grow similarly and stay red. have you tasted them - do they remain hard , red and sour?

Have they been growing in the same place for a long time? The usual reason for fruit not ripening is shortage of potash. Try giving them a good dressing of this at the start of the growing season. It might just do the trick & all fruit needs it whatever the type.