This “blob of white stuff” on a blackcurrant bush is actually the egg mass of the woolly scale insect (Pulvinaria ribesiae).
Scale insects are sap feeders, like aphids. If a plant is severely infested, the sap sucking can weaken it. The honeydew produced by the scale insects can also encourage mould growth. However, most often, scale insects are not a major problem.
There are many other types of scale insect in addition to the woolly one: generally, they’re quite hard to spot as they attach to the stem like a limpet – and even when you find the scales, often they’re just the empty cases of dead insects.
If you do want to get rid of the scale insects, scrubbing or picking them off is probably the best way. You can also prune out the affected wood and burn it. As ever, don’t forget that the good insects and other predators in your garden do need some bad ones to feed on; so it’s often advisable to put up with low levels of “pests”.