Now I'm the first to point out that we don't want to arbitrarily kill off insects in the garden - for example ants are brilliant for aerating the soil and, funnily enough, cleaning up damage that other critters have done to your plants. That said, if I'm not getting any blackcurrants, then they have to go.
Trying to find a natural solution that won't harm my kids or my dog, I stumbled across diatomaceous earth - which is the fossilised remains of marine phytoplankton. Funnily enough I already have about 5kg of it as we feed it to our dog to prevent worms, ticks and fleas. Even the food grade stuff is very economical, and won't hurt if ingested. You do want to be careful not to breathe it in though as it isn't very good for the membranes in your lungs.
I suggest leaving kids and pets indoors whilst you apply it.
I literally put two tablespoons in a sieve and tap the edge of the sieve to make a 'snow storm' over my plants, always standing up wind. You may need to apply a few times a week initially, but after that it will be done :0)
Very easy, very cheap and very effective.
The way DE works on insects, like ants, is that on a microscopic level it is very sharp. It punctures the waxy layer on the insects exoskeleton and dries them out (sorry little ants!). This is important because it is a PHYSICAL way of killing them, not chemical. In the first place, this is better for my kids and pets because there are no nasty chemicals flying around; secondly, it's good for my garden because you can't build up a tolerance to a physical death, meaning we don't end up with super resilient bugs that we can't get rid of in our gardens; thirdly I like is because it simply breaks down into the soil and actually adds nutrients.