Leaf curl on Blackcurrant bushes - what to do?

Sounds like it could be aphids. Uncurl the leaves and see if you have any of the little critters inside. A severe infestation can be quite a problem so you need to get rid of them. Some people recommend spraying with soapy water which may or may not get rid of them but will certainly give you clean aphids!

Whether you go down the organic or non-organic route you need to get on top of it.