Hi,
I also inherited some neglected black currant bushes when I took over my allotment, although not as tall as yours. After a very poor harvest I decided I had nothing to loose so I cut them down to 6” above ground and gave each bush a 4-5” mulch of compost. The following year produced lots of new growth and not much fruit but by the second year they fruited very well. Now I prune and mulch them every year as normal. I am obliged to replace any of these bushes that die because they border the main path through our site. Because of this, when I cut them back I took plenty of cuttings in case the parent plant didn’t recover. Judging by your photograph you have plenty of cutting material so that might be prudent, just in case. Good luck.
