The ideal situation is to create an environment where aphid eaters are present to deal with them. Some predators of aphids are ladybirds and ground beetles. Earwigs will also munch on them too.
If you can bear to do it, aphid colonies can be squashed between a finger and thumb.
Some people advocate picking off the soft shoot stem containing most of the blackfly at the top of the plant.
There are some organic sprays available containing natural pyrethrum and plant oils that can be used. Those containing plant oil are less likely to negatively affect adult ladybirds.
Try to avoid using pesticides as these can also kill off the blackfly’s natural predators. However, if you do decide to use them, follow the instructions to use very carefully. Also, do not spray on plants in flower as the sprays can harm and/or kill bees and other pollinating insects.
To stay one step ahead, there are a couple of companion plants that can prevent aphids from feasting on your vegetable garden.
Alliums like onions, garlic, leeks, and chives have a strong fragrance that repels aphids.
Then, planting marigolds can drive a variety of pests away including cabbage moths and cabbage white butterflies, once again because of the strong scent.