Jeni: It maybe no use to you to know, but I have a similar situation in my daughter-in-law’s veg garden (neglected for years) though in this case there is little couch grass, but aggressive ground elder, brambles and stinging nettles substitute adequately for it! There’s even a bit of Japanese knotweed to add to the fun! (That seems to be too intimidated by the ground elder and brambles to do its usual stunts!) The blackcurrant bushes have fruited pretty well (without any attention from me or others apart from cutting back too aggressive brambles) for several years – I have simply pruned them at the right time. We just haven’t had time, because it’s very large garden, (and I have my own to deal with as well) to get around to clearing this part of the ground. i have used a sickle on the weeds in summer largely to make it possible to get to the bushes to harvest them. I haven’t so far covered anything, nor have I composted the area, which is under mature apple and pear trees. No doubt if I followed Charles’s advice we’d get even better crops. I still haven’t quite worked out how he gets all the compost and other material to cover the areas he does. E.g.
http://www.charlesdowding.co.uk/no-dig-growing/no-dig-growing-preparation/
I suppose if you have enough cardboard you could cut it to fit tightly to the stems of the blackcurrants? If every plant else is in the dark and the blackcurrants have all the light, that should give them quite an advantage? Nice idea of Manbikeveg’s to use some of the couch grass against itself as a compost! The same could be done with my stinging nettles (which are particularly useful for their nutrients) but I’ve learnt from experience not to try composting them when seeding – that year I just got stinging nettles coming up all over the place – not nice to weed among!
Good Luck
Marcus