It is the caterpillars which do the damage rather than the moths or butterflies. The damage occurs between April and October because each of the varieties has two or more generations from spring to autumn. 

 

The life cycle is as follows. The adults appear in mid-spring and lay single eggs on the leaves of cabbage, cauliflower, Brussels sprouts, kale and kohlrabi. The eggs are yellow, oblong and ridged lengthwise. They hatch in around 5 days depending on weather conditions. Initially they feed on the outer leaves, but as they mature, they tend to go for the heart leaves. They reach about 2.5 cms (1 inch) in length after a couple of weeks. Around this stage they pupate into a chrysalis and it is from these chrysalis that more butterflies and moths will emerge. The final generation of each year over-winters as a chrysalis.

The caterpillars can be identified as follows:

Cabbage Moth - green-brown all over with no 'hair'
Large Cabbage White - a yellow body with dark black markings all over the body.
Small Cabbage White - these are pale green all over with a velvet looking texture.

The damage is caused by them eating the leaves, both the outer leaves and more annoyingly leaves at the heart of cabbages. The holes are no particular shape and are irregular.  

How to Treat Cabbage Whitefly
These caterpillars can cause considerable damage to cabbage plants especially if they get to the heart leaves. It really is best to keep a regular check going for damage and take action immediately it is noticed. The best solution is to remove the caterpillars by hand when they are young and still on the outer leaves. 

An alternate solution is to protect the plants with netting or some other form of covering especially made for the purpose. These are readily available from nurseries, garden centres and DIY stores. A spraying with derris will also help and will not cause damage to wildlife.

Once the caterpillars have got to the heat of the cabbage, it's very difficult to treat with anything but chemicals. Spray with an approved chemical but follow the instructions on the packet carefully.