This family, called the Brassicas, tend to be more susceptible to attack from the Cabbage Moth and the Cabbage White Butterfly when conditions are too warm for them or when the soil they are growing in is too acid for their liking, especially while the plants are young.
The cabbage family includes Brussels sprouts, Chinese cabbage, cauliflower, horseradish, kale, kohlrabi, mizuna, mustard greens, swede, tatsoi, turnip, watercress and stock, and is also related to radish. These plants need both boron and molybdenum for healthy growth and these are only available to plants when the soil pH is close to neutral. If you know that your soil is acid, and your Brassica plants are being attacked, give the bed a drink of dolomite or agricultural lime. Dissolve a generous handful in a full watering can and apply this to each square metre of the bed. Repeat the application if pests are still hanging around in two weeks.
In the meantime, remove all pest eggs from under leaves and leave crushed caterpillars on the leaves. This helps to deter further egg laying.